From History of the Catholic Church: From the Apostolic Age to the Third Millennium, by James Hitchcock (2012), p. 41:
As a young priest, Irenaeus came to Rome to consult the bishop. He also thought it appropriate to record the names of all the bishops of Rome to his own day, the first three of whom—St. Linus (67-76), Cletus (76-91), and Clement (91-100)—are still commemorated in the Roman liturgy immediately following the Apostles themselves.[Note: I link to this blog page from my Amazon.com "customer review" of Hitchcock's book.]
Compare Hitchcock's terse mention of Irenaeus's list with what follows below. Hitchcock's book is, admittedly, a broad survey covering two millennia, with scant room for extensive treatment of any single topic. Further, his target audience is Catholic believers, which seems to diminish his need for historical objectivity. The unfortunate result is a book that, in addition to ostensibly being history, is also advocacy and apologetics—delivered to an audience that's sure to be oblivious to the missing nuance, caveats, and deeper explanations. And so that single-sentence mention of Irenaeus's list strikes me as egregiously misleading, serving inevitably to reinforce the casual reader's belief in an unbroken line of popes (holding the office of bishop of Rome) extending back to Peter: a belief at odds with the preponderance of evidence and with scholarly consensus. If such a thing is to be believed at all, it must be believed on faith, and not as a demonstrable historical fact.
From The Future of the Catholic Church With Pope Francis, by Garry Wills (2015), pp. 102-103:
Originally, succession was not only uncertain in method but sketchily recorded. The Roman church, not having a bishop until the second century, could not have recorded a line of bishops before that. The list was confected in retrospect, as Eamon Duffy says, "based on scraps of half-remembered information, or simply invented." The aim was not history but symbol: [quote from Duffy here, followed by endnote: Eamon Duffy, Saints and Sinners: A History of the Popes, third edition, (Yale University Press, 2006), 26] In short, where records were lacking, they were simply made up.
From The Catholic Church: A Short History, by Hans Küng (2001), pp. 23-24:
It cannot be verified that the bishops are successors of the apostles in the direct and exclusive sense. It is historically impossible to find in the initial phase of Christianity an unbroken chain of laying on of hands from the apostles to the present-day bishops. Historically, rather, it can be demonstrated that in the first postapostolic phase, local presbyter-bishops became established alongside prophets, teachers, and other ministers as the sole leaders of the Christian communities (and also at the celebration of the Eucharist); thus a division between "clergy" and "laity" took place at an early stage. In a further phase the monarchical episcopate, of an individual bishop, increasingly displaced a plurality of presbyter-bishops in a city and later throughout the region of a church. In Antioch around 110, with Bishop Ignatius there came into being the order of three offices which later became customary all over the empire: bishop, presbyter, and deacon. The Eucharist could no longer be celebrated without a bishop. The division between the clergy and the people was now a fact.
But it is striking that Ignatius, this defender and ideologue of the monarchical episcopate, did not address a bishop in his letter to the Roman community, any more than Paul did. And there was no mention of a bishop in Rome in any other of the earliest sources, like the Letter of Clement (around 90).
However, the earliest list of bishops, in Irenaeus of Lyons, according to which Peter and Paul transferred the ministry of episkopos to a certain Linus, is a second-century forgery. A monarchical episcopate can be demonstrated for Rome only from around the middle of the second century (Bishop Anicetus).
From Keepers of the Keys of Heaven, by Roger Collins (2009), p. 10:
Admittedly, there is still a gap of a century to a century and a half between the presumed period in which Peter and Paul were in Rome and the time at which Irenaeus and others were writing [endnote: Jean-Pierre Martin, 'Sixte Ier', in Levillain, 1588]. Ultimately, however, the testimony of these writers was in error, for the office of bishop, as Irenaeus and Tertullian understood it, simply did not exist in the time of Peter and Paul.p. 14:
The late-second century authors were probably reporting on a tradition that had grown up in Rome in which leading figures amongst the elders of their day were retrospectively turned into bishops, to produce a continuous list of holders of the office stretching back to Peter. Why this happened can be explained, but it would be helpful to ask which of the people named by Irenaeus and Tertullian should be regarded as the first real bishop of the city. Most scholars now agree that the answer would be Anicetus, who comes in tenth on both lists, and whose episcopate likely covered the years 155 to 166. [endnote: Lampe, Peter, From Paul to Valentinus: Christians at Rome in the First Two Centuries, (English tr. Minneapolis, 2003), 397-408]p. 15:
This may explain why Irenaeus and Tertullian's apparent rewriting of the history of Christianity in Rome provoked no evident disagreement. Why they were so keen to present the Roman church as one ruled by an unbroken succession of bishops since the time of the Apostles is another matter. What is significant is that both authors produced their lists of bishops in writings that were explicitly controversial and intended to combat theological opponents. Neither was interested in the history of the Church in Rome for its own sake. The existence of the line of bishops they described was a central plank in their arguments. Both were appealing to it as a source of authority to be preferred to that claimed by their adversaries, the Gnostics.
Update 2015-05-11 - The first dozen pages of Eamon Duffy's Saints and Sinners: A History of the Popes (first ed.) is available online. It's an excellent read, and I highly recommend it.