Here is an excerpt from Joseph Cardinal Ratzinger's book Called To Communion:
The principle of succession in general
That the primacy of Peter is recognizable in all the major strands of the New Testament is incontestable.
The real difficulty arises when we come to the second question: Can the idea of a Petrine succession be justified? Even more difficult is the third question that is bound up with it: Can the Petrine succession of Rome be credibly substantiated?
Concerning the first question, we must first of all note that there is no explicit statement regarding the Petrine succession in the New Testament. This is not surprising, since neither the Gospels nor the chief Pauline epistles address the problem of a postapostolic Church—which, by the way, must be mentioned as a sign of the Gospels' fidelity to tradition. Indirectly, however, this problem can be detected in the Gospels once we admit the principle of form critical method according to which only what was considered in the respective spheres of tradition as somehow meaningful for the present was preserved in writing as such. This would mean, for example, that toward the end of the first century, when Peter was long dead, John regarded the former's primacy, not as a thing of the past, but as a present reality for the Church.
For many even believe—though perhaps with a little too much imagination—that they have good grounds for interpreting the "competition" between Peter and the beloved disciple as an echo of the tensions between Rome's claim to primacy and the sense of dignity possessed by the Churches of Asia Minor. This would certainly be a very early and, in addition, inner-biblical proof that Rome was seen as continuing the Petrine line; but we should in no case rely on such uncertain hypotheses. The fundamental idea, however, does seem to me correct, namely, that the traditions of the New Testament never reflect an interest of purely historical curiosity but are bearers of present reality and in that sense constantly rescue things from the mere past, without blurring the special status of the origin.
Moreover, even scholars who deny the principle itself have propounded hypotheses of succession. 0. Cullmann, for example, objects in a very clear-cut fashion to the idea of succession, yet he believes that he can Show that Peter was replaced by James and that this latter assumed the primacy of the erstwhile first apostle. Bultmann believes that he is correct in concluding from the mention of the three pillars in Galatians 2:9 that the course of development led away from a personal to a collegial leadership and that a college entered upon the succession of Peter. 
We have no need to discuss these hypotheses and others like them; their foundation is weak enough. Nevertheless, they do show that it is impossible to avoid the idea of succession once the word transmitted in Scripture is considered to be a sphere open to the future. In those writings of the New Testament that stand on the cusp of the second generation or else already belong to it-especially in the Acts of the Apostles and in the Pastoral Letters—the principle of succession does in fact take on concrete shape.
The Protestant notion that the "succession" consists solely in the word as such, but not in any "structures", is proved to be anachronistic in light of what in actual fact is the form of tradition in the New Testament. The word is tied to the witness, who guarantees it an unambiguous sense, which it does not possess as a mere word floating in isolation. But the witness is not an individual who stands independently on his own. He is no more a wit ness by virtue of himself and of his own powers of memory than Peter can be the rock by his own strength. He is not a witness as "flesh and blood" but as one who is linked to the Pneuma, the Paraclete who authenticates the truth and opens up the memory and, in his turn, binds the witness to Christ. For the Paraclete does not speak of himself, but he takes from "what is his" (that is, from what is Christ's: Jn 16: 13).
This binding of the witness to the Pneuma and to his mode of being-"not of himself, but what he hears" -is called "sacrament" in the language of the Church. Sacrament designates a threefold knot-word, witness, Holy Spirit and Christ-which describes the essential structure of succession in the New Testament. We can infer with certainty from the testimony of the Pastoral Letters and of the Acts of the Apostles that the apostolic generation already gave to this interconnection of person and word in the believed presence of the Spirit and of Christ the form of the laying on of hands.
The Petrine succession in Rome
In opposition to the New Testament pattern of succession described above, which withdraws the word from human manipulation precisely by binding witnesses into its service, there arose very early on an intellectual and anti-institutional model known historically by the name of Gnosis, which made the free interpretation and speculative development of the word its principle. Before long the appeal to individual witnesses no longer sufficed to counter the intellectual claim advanced by this tendency. It became necessary to have fixed points by which to orient the testimony itself, and these were found in the so-called apostolic sees, that is, in those where the apostles had been active. The apostolic sees became the reference point of true communio. But among these sees there was in turn–quite clearly in Irenaeus of Lyons–a decisive criterion that recapitulated all others: the Church of Rome, where Peter and Paul suffered martyrdom. It was with this Church that every community had to agree; Rome was the standard of the authentic apostolic tradition as a whole.
Moreover, Eusebius of Caesarea organized the first version of his ecclesiastical history in accord with the same principle. It was to be a written record of the continuity of apostolic succession, which was concentrated in the three Petrine sees Rome, Antioch and Alexandria-among which Rome, as the site of Peter's martyrdom, was in turn preeminent and truly normative. 
This leads us to a very fundamental observation.  The Roman primacy, or, rather, the acknowledgement of Rome as the criterion of the right apostolic faith, is older than the canon of the New Testament, than "Scripture".
We must be on our guard here against an almost inevitable illusion. "Scripture" is more recent than "the scriptures" of which it is composed. It was still a long time before the existence of the individual writings resulted in the "New Testament" as Scripture, as the Bible. The assembling of the writings into a single Scripture is more properly speaking the work of tradition, a work that began in the second century but came to a kind of conclusion only in the fourth or fifth century. Harnack, a witness who cannot be suspected of pro-Roman bias, has remarked in this regard that it was only at the end of the second century, in Rome, that a canon of the "books of the New Testament" won recognition by the criterion of apostolicity-catholicity, a criterion to which the other Churches also gradually subscribed "for the sake of its intrinsic value and on the strength of the authority of the Roman Church".
We can therefore say that Scripture became Scripture through the tradition, which precisely in this process included the potentior principalitas–the preeminent original authority–of the Roman see as a constitutive element.
Two points emerge clearly from what has just been First, the principle of tradition in its sacramental form-apostolic succession—played a constitutive role in the existence and continuance of the Church. Without this principle, it is impossible to conceive of a New Testament at all, so that we are caught in a contradiction when we affirm the one while wanting to deny the other. Furthermore, we have seen that in Rome the traditional series of bishops was from the very beginning recorded as a line of successors.
We can add that Rome and Antioch were conscious of succeeding to the mission of Peter and that early on Alexandria was admitted into the circle of Petrine sees as the city where Peter's disciple Mark had been active. Having said all that, the site of Peter's martyrdom nonetheless appears clearly as the chief bearer of his supreme authority and plays a preeminent role in the formation of tradition which is constitutive of the Church-and thus in the genesis of the New Testament as Bible; Rome is one of the indispensable internal and external- conditions of its possibility. It would be exciting to trace the influence on this process of the idea that the mission of Jerusalem had passed over to Rome, which explains why at first Jerusalem was not only not a "patriarchal see" but not even a metropolis: Jerusalem was now located in Rome, and since Peter's departure from that city, its primacy had been transferred to the capital of the pagan world. 
But to consider this in detail would lead us too far afield for the moment. The essential point, in my opinion, has already become plain: the martyrdom of Peter in Rome fixes the place where his function continues. The awareness of this fact can be detected as early as the first century in the Letter of Clement, even though it developed but slowly in all its particulars.
We shall break off at this point, for the chief goal of our considerations has been attained. We have seen that the New Testament as a whole strikingly demonstrates the primacy of Peter; we have seen that the formative development of tradition and of the Church supposed the continuation of Peter's authority in Rome as an intrinsic condition. The Roman primacy is not an invention of the popes, but an essential element of ecclesial unity that goes back to the Lord and was developed faithfully in the nascent Church.
But the New Testament shows us more than the formal aspect of a structure; it also reveals to us the inward nature of this structure. It does not merely furnish proof texts, it is a permanent criterion and task. It depicts the tension between skandalon and rock; in the very disproportion between man's capacity and God's sovereign disposition, it reveals God to be the one who truly acts and is present.
If in the course of history the attribution of such authority to men could repeatedly engender the not entirely unfounded suspicion of human arrogation of power, not only the promise of the New Testament but also the trajectory of that history itself prove the opposite. The men in question are so glaringly, so blatantly unequal to this function that the very empowerment of man to be the rock makes evident how little it is they who sustain the Church but God alone who does so, who does so more in spite of men than through them.
The mystery of the Cross is perhaps nowhere so palpably present as in the primacy as a reality of Church history. That its center is forgiveness is both its intrinsic condition and the sign of the distinctive character of God's power. Every single biblical logion about the primacy thus remains from generation to generation a signpost and a norm, to which we must ceaselessly resubmit ourselves. When the Church adheres to these words in faith, she is not being triumphalistic but humbly recognizing in wonder and thanksgiving the victory of God over and through human weakness. Whoever deprives these words of their force for fear of triumphalism or of human usurpation of authority does not proclaim that God is greater but diminishes him, since God demonstrates the power of his love, and thus remains faithful to the law of the history of salvation, precisely in the paradox of human impotence.
For with the same realism with which we declare today the sins of the popes and their disproportion to the magnitude of their commission, we must also acknowledge that Peter has repeatedly stood as the rock against ideologies, against the dissolution of the word into the plausibilities of a given time, against subjection to the powers of this world.
When we see this in the facts of history, we are not celebrating men but praising the Lord, who does not abandon the Church and who desired to manifest that he is the rock through Peter, the little stumbling stone: "flesh and blood" do not save, but the Lord saves through those who are of flesh and blood. To deny this truth is not a plus of faith, not a plus of humility, but is to shrink from the humility that recognizes God as he is. Therefore the Petrine promise and its historical embodiment in Rome remain at the deepest level an ever-renewed motive for joy: the powers of hell will not prevail against it . . .
 Die Geschichte der synoptischen Tradition, 2d ed. (198 1), 147- 51; cf. Gnilka, 56.
 For an exhaustive account of this point, see V. Twomey, Apostolikos Thronos (Münster, 1982).
 It is my hope that in the not-too-distant future I will have the opportunity to develop and substantiate in greater detail the view of the succession that I attempt to indicate in an extremely condensed form in what follows. I owe important suggestions to several works by 0. Karrer, especially: Um die Einheit der Christen. Die Petrusfrage (Frankfurt am Mainz, 1953); "Apostolische Nachfolge und Primat", in: Feiner, Trütsch and Böckle, Fragen in der Theologie heute (Freiburg im.Breisgau, 1957), 175-206; "Das Petrusamt in der Frühkirche", in Festgabe J. Lortz (Baden-Baden, 1958), 507-25; "Die biblische und altkirchliche Grundlage des Papsttums", in: Lebendiges Zeugnis (1958), 3-24. Also of importance are some of the papers in the festschrift for 0. Karrer: Begegnung der Christen, ed. by Roesle-Cullmann (Frankfurt am Mainz, 1959); in particular, K. Hofstetter, "Das Petrusamt in der Kirche des I. und 2. Jahrhunderts", 361-72.
 Cf. Hofstetter.
Hat tip to Ignatius Insight.