When scholars refer to the “Synoptic Problem,” they mean the literary relationship between the first three canonical gospels. Matthew, Mark, and Luke retell the story of Jesus in a very similar manner (syn =together, opsis = view), whereas the Gospel of John is quite different from the “Synoptic” tradition. Indeed, there must be some kind of literary relationship since the Synoptic Gospels often agree in order, wording, and even parenthetical asides such as “let the reader understand” (Mark 13:14; Matt 24:14). To see this literary relationship clearly, the best thing a student of the New Testament can do is grab a Synopsis and compare any single story that appears in all three Gospels (i.e. “triple tradition”). Or you can compare the predominantly sayings material that Matthew and Luke have in common but is not in Mark (i.e. “double tradition”).
The most common solutions to this tricky puzzle are the Griesbach hypothesis (Matthew and Luke wrote first with Mark as a later abridgement of the two), the Two Source Hypothesis (Mark wrote first and was independently used by Matthew and Luke, while the double tradition goes back to a single Greek document labelled “Q” from the German Quelle or source), and the Farrer or Goulder-Goodacre hypothesis (Mark wrote first and was used by Matthew and Luke, while Luke also used Matthew so there is no need for “Q”). There are more chaotic approaches to the Synoptic problem that may allow for Luke’s knowledge of Matthew as well as that some of the double tradition may go back to a variety of Greek and Aramaic oral and written sources. For more in depth treatment, see Stephen Carlson’s excellent site on the Synoptic Problem, including a number of diagrams of potential solutions and an annotated bibliography. Or Mark Goodacre, who made his introductory textbook The Synoptic Problem: A Way Through the Maze available online, has many useful podcasts on this question.
Most Patristic commentators accepted Matthean priority, which is also first in the order of the Four Gospel Canon, and Augustine’s solution that Mark was a follower and abbreviator of Matthew (De Consensu Evangelistarum 1.3) held sway for roughly 1400 years. Griesbach supporters point to a comment by Clement of Alexandria (in Eusebius, Ecclesiastical History 6.14.5) that the Gospels with the genealogies (=Matthew and Luke) came first, though Stephen Carlson has offered an alternative translation (cf. “Clement of Alexandria on the ‘Order’ of the Gospels” NTS 47 : 118-25 ). The Griesbach hypothesis is a minority view and is supported online at The Two Gospels Hypothesis Website or Geoff Trowbridge’s summary of William Farmer’s arguments. I am in agreement with the vast majority of NT scholars, both in the Two Source and Farrer camps, on Markan priority. The arguments from order (Mark tends to be the middle term as Matthew and Luke rarely agree in wording or order against Mark), length (Mark is the shortest of the three and almost entirely reproduced in Matthew and Luke), style (Matthew/Luke edit and clean up Mark’s awkward grammar or style, omit Aramaic words, etc), and harder readings (Matthew/Luke edit Mark’s statements on Christology, eschatology, the disciples, and so on). Further, Mark makes an odd summary of Matthew or conflation of Matthew/Luke: why would Mark cut out the birth narratives, much of the ethical teaching (e.g., Sermon on the Mount or Plains), and the resurrection appearances after Mark 16:8? Why would Mark add details to individual triple tradition pericopes such as that Jesus’ family had thought he had gone out of his mind (Mark 3.19-21), that Jesus’ initial attempt to heal the blind man was not fully successful (‘I can see people, but they look like trees, walking.’) (Mark 8:22-25), that the fig tree Jesus cursed for not having any fruit because “it was not the season for figs” (Mark 11:14), that a naked youth fled from the garden of Gethsemane (Mark 14:51-52), or references to Jesus’ emotions (Mark 1:41; 3:5)? It makes sense for Matthew and Luke to insert birth, didactic and resurrection traditions while omitting other potentially embarrassing details in Mark. Here are examples where Mark seems to be the earlier account:
And he did not do many mighty works there, because of their unbelief (Matthew 13.58)
And he could do no mighty work there, except that he laid his hands upon a few sick people and healed them. And he marveled because of their unbelief. (Mark 6.5-6)
“Save, Lord; we are perishing!” (Matt 8.25)
“Teacher, do you not care if we perish?” (Mark 4.38)
“Master, Master, we are perishing!” (Luke 8.24)
‘Truly I say to you, there are some standing here who will not taste death before they see the Son of Man coming in his kingdom.’ (Matthew 16.28)
And he said to them, ‘Truly I tell you, there are some standing here who will not taste death before they see that the kingdom of God has come with power.’ (Mark 9.1)
Then Jesus was led up by the Spirit into the wilderness… (Matthew 4:1; cf. Luke 4:1)
The Spirit immediately drove [from ekballō] him out into the wilderness (Mark 1:12)
“Why do you ask me about what is good? One there is who is good.” (Matt 19:17)
“Why do you call me good? No one is good but God alone.” (Mark 10:18; cf. Luke 18:19)
…and behold a leper came to him and knelt before him, saying, ‘Lord, if you will, you can make me clean.’ And he stretched out his hand and touched him, saying, ‘I will; be clean!’ (Matthew 8.2-3)
And a leper came to him beseeching him, and kneeling said to him, ‘If you will, you can make me clean.’ Moved with anger [textual variant: compassion; see here for more discussion], Jesus stretched out his hand and touched him, and said to him, ‘I will; be clean!’ (Mark 1.40-42)
…when he saw Jesus, he fell on his face and besought him, ‘Lord, if you will, you can make me clean.’ And he stretched out his hand and touched him, and said, ‘I will; be clean.’ (Luke 5.12-13).
But when the crowd had been put outside, he went in and took her by the hand, and the girl got up. (Matt 9:25)
He took her by the hand and said to her, ‘Talitha cum’, which means, ‘Little girl, get up!’ (Mark 5:41)
But he took her by the hand and called out, ‘Child, get up!’ (Luke 8:54)
*Aramaic words in Mark 3:17; 5:41; 7:11, 34; 14:36; 15:22, 34.
He said to them, ‘Have you not read what David did when he and his companions were hungry? He entered the house of God and ate the bread of the Presence, which it was not lawful for him or his companions to eat, but only for the priests… [omits Mark 2:27] For the Son of Man is lord of the sabbath. (Matt 12:3-4, 8.)
And he said to them, ‘Have you never read what David did when he and his companions were hungry and in need of food? He entered the house of God, when Abiathar was high priest, and ate the bread of the Presence, which it is not lawful for any but the priests to eat, and he gave some to his companions.’ Then he said to them, ‘The sabbath was made for humankind, and not humankind for the sabbath; so the Son of Man is lord even of the sabbath.’ (Mark 2:25-28)
Jesus answered, ‘Have you not read what David did when he and his companions were hungry? He entered the house of God and took and ate the bread of the Presence, which it is not lawful for any but the priests to eat, and gave some to his companions?’ [omits Mark 2:27] Then he said to them, ‘The Son of Man is lord of the sabbath.’ (Luke 6:3-5)
But when the disciples saw him walking on the lake, they were terrified, saying, ‘It is a ghost!’ And they cried out in fear. But immediately Jesus spoke to them and said, ‘Take heart, it is I; do not be afraid.’ Peter answered him, ‘Lord, if it is you, command me to come to you on the water.’ He said, ‘Come.’ So Peter got out of the boat, started walking on the water, and came towards Jesus. But when he noticed the strong wind, he became frightened, and beginning to sink, he cried out, ‘Lord, save me!’ Jesus immediately reached out his hand and caught him, saying to him, ‘You of little faith, why did you doubt?’ When they got into the boat, the wind ceased. And those in the boat worshiped him, saying, ‘Truly you are the Son of God.’ (Matt 14:26-33)
But when they saw him walking on the lake, they thought it was a ghost and cried out; for they all saw him and were terrified. But immediately he spoke to them and said, ‘Take heart, it is I; do not be afraid.’ Then he got into the boat with them and the wind ceased. And they were utterly astounded, for they did not understand about the loaves, but their hearts were hardened. (Mark 6:49-52)
[omitted in Luke]
‘So when you see the desolating sacrilege standing in the holy place, as was spoken of by the prophet Daniel (let the reader understand), then those in Judea must flee to the mountains. (Matt 24:15-16)
‘But when you see the desolating sacrilege set up where it ought not to be (let the reader understand), then those in Judea must flee to the mountains. (Mark 13:14)
‘When you see Jerusalem surrounded by armies, then know that its desolation has come near. Then those in Judea must flee to the mountains (Luke 21:20-21a)
As they went out, they came upon a man from Cyrene named Simon; they compelled this man to carry his cross (Matt 27:32)
They compelled a passer-by, who was coming in from the country, to carry his cross; it was Simon of Cyrene, the father of Alexander and Rufus (Mark 15:21)
As they led him away, they seized a man, Simon of Cyrene, who was coming from the country, and they laid the cross on him, and made him carry it behind Jesus. (Luke 23:26)
There are many more examples that could be given, but these examples suffice to convince me that Markan priority is the most likely scenario. One sign of the consensus on Markan priority is that, of all the commentaries I listed here, the vast majority start from the premise of Markan priority. The one significant exception is C.S. Mann’s commentary on Mark for the Anchor Bible series that worked on the basis of the Griesbach hypothesis, but it has been replaced by Joel Marcus’s two-volume commentaries that is firmly in support of Markan priority (Mark 1-8, pp. 40-47). A “consensus” can always be overturned, but to defeat a reigning paradigm one must 1. poke enough holes into its main arguments and 2. present enough counter-arguments to suggest another solution is more probable. I do not see that happening any time soon.