The overlaps between Matthew, Mark and Luke are too close for coincidence and too uneven for simple copying. The dominant solution is Markan priority: Mark was written first and used independently by Matthew and Luke, who also drew several hundred verses of shared material, mostly sayings, that Mark lacks. That common material is conventionally attributed to a lost source labelled Q, from the German Quelle. Matthew and Luke each additionally carry material unique to them.
Q is a hypothesis, not a manuscript. No copy has ever been found and no ancient writer mentions it. The main alternative, the Farrer hypothesis, keeps Markan priority but dispenses with Q by proposing that Luke read and reworked Matthew; it has been argued at length by Michael Goulder and Mark Goodacre and has a real following. A minority still defends Matthean priority, the traditional order. Markan priority itself is close to consensus; Q is majority opinion with active dissent.
Dating rests largely on internal evidence. Most critical scholars place Mark around 65 to 75 CE, near the Jewish revolt and the destruction of the Temple in 70; Matthew and Luke in the 80s or 90s; and John in the 90s or slightly later. Conservative scholars argue for earlier dates, in some cases before 70, noting among other things that Acts ends with Paul alive under house arrest in Rome and says nothing of his death or of the Temple's fall.
The gospels are formally anonymous. The names attached to them are not in the texts and appear in the manuscript tradition from the later second century. Traditional attribution holds that Matthew the tax collector, Mark the interpreter of Peter, Luke the companion of Paul and John the beloved disciple wrote them; most critical scholars regard the titles as second-century ascriptions and the authors as unknown.