Wenham, John. "Chapter Six: Ancient Testimony to Mark's Gospel." Redating Matthew, Mark, and Luke: A Fresh Assault on the Synoptic Problem. Downers Grove, Illinois: InterVarsity Press, 1992, 136-145.
As with Matthew's Gospel, ancient testimony about Mark's Gospel begins with Papias, quoted by Eusebius. Papias' report is that John (possibly the apostle but called the Presbyter) said Mark wrote the report of what Peter said about the Lord (Wenham 1992, 136). Eusebius considered Matthew to show an orderly, literary polish, while Mark he considered more influenced by orality. The testimony that Mark wrote in Rome under the influence of Peter is quite solid.
Wenham considers it significant that Papias calls Mark the ἑρμηνευτής, or "interpreter" of Peter (Wenham 1992, 137). This does not strike Wenham as a word used of a transcriptionist but of someone who would engage in additional teaching. Papias considered the account accurate and a full account, though not in order (Wenham 1992, 138).
Wenham notes that Irenaeus described Mark as writing during Peter's life, at a time close to the preaching, but that he passed the written account on only afte rPeter's death (Wenham 1992, 139). This emphasizes Mark's writing as coming while Peter could affirm his accuracy.
In addition to his quotes of Papias, Eusebius helpfully quotes Clement of Alexandria, who understood Mark to have written according to Peter's speech, with Peter's knowledge (H.E. 6.14.6f, Wenham 1992, 141). Eusebius also quotes Origen's commentary on Matthew, in which Origen states he learned of four Gospels. He takes Mark to have written what Peter taught (H.E. 6.25.5, Wenham 1992, 142).