When were the gospels written and by whom?

There are a number of different sources addressing this. I'll mention just two. Documents from the Vaults of the Vatican have recorded the sermons of all the early Christian Fathers, most of which we're not permitted to see. Right up until just after half-way through the second century, none of them quoted from any of the four gospels. Justin Martyr, the most eminent of these, from the middle of the second century, used more than 300 quotations from the Old Testament & nearly 100 quotations from the Apocryphal books, but none from any of the four gospels we now have or any resemblance thereof. The Catholic Church best dates that the Holy Bible was written & published between the time of Justin & Papias, & the time of Theophilus & Irenaeus. That should cover the "when" part of your question, which is also covered in more detail in "The Christ", by John E Remsberg. Scholars & the Churches agree that these books are anonymous. They do not purport to have been written by Matthew, Mark, Luke & John. Their titles don't affirm it. They simply imply they are simply "according" to the supposed teachings of these evangelists. Renan puts it thus: "they merely signify that these were the traditions proceeding from each of these apostles, & claiming their authority". Rev. Dr. Hooykaas says: "They appeared anonymously. The titles placed above them in our Bibles owe their origin to a later ecclesiastical tradition which deserves no confidence whatsoever". This is from "The Bible for Learners", volume 3, page 24. It is claimed that Matthew's Gospel appeared originally in Hebrew. Our version is a translation of a Greek work. St Jerome, the famous early Catholic Translator, says: "Who afterwards translated it into Greek is not sufficiently certain". From this, Michaelis concludes, "If the original text of Matthew is lost, & we have nothing but a Greek translation then, frankly, we cannot ascribe any divine inspiration to the words". The contents of these Gospels refute the claim that they were written by the named evangelists. Each of them narrates events & contain doctrinal teachings belonging to a much later age. Matthew's Gospel tells us Jesus said, "Thou art Peter, & Upon this rock I will build my Church" (xvi,18). This Gospel is a Roman Catholic Gospel & was written after the beginning of the establishment of this hierarchy to uphold the supremacy of the Petrine Church of Rome. One of Germany's greatest theologians, Dr. Schleiermacher, concludes his detailed works that Luke is just a compilation of 33 preexisting manuscripts (page 313). Other Bible Scholars conclude that Luke is based on the Gospel of Marcion, a Second Century work based on St Paul's writings. The Rev. S. Baring-Gould in his work, Lost & Hostile Gospels, says "the arrangement is so similar that we are forced to the conclusion that it was either used by St Luke or that it was his original composition. If he used it then his right to the title of Author of the Third Gospel falls to the ground, as what he added was of small amount". Mark, according to Renan, is the oldest of the Gospels, but was written after Matthew & Luke, according to Strauss, who writes, "it is evidently a compilation, whether made from memory or otherwise, from the first & third Gospels" (Leben Jesu, pg5I). Davidson declares it to be an anonymous work. The internal evidence against the authenticity of the fourth Gospel is conclusive. The Apostle John did not write it. John, the Apostle, was a Jew; the author of the fourth Gospel was not a Jew. John was born in Bethsaida; the author of the fourth Gospel did not know where Bethsaida was located. John was an uneducated fisherman; the author of the fourth Gospel was an accomplished scholar. Some of the most important events in the life of Jesus, the other Gospels declare, were witnessed by John; the author of this Gospel knows nothing of these events. The Apostle John witnessed the Crucifixion; the author of this Gospel did not. All the Apostles, including John, believed Jesus to be a man; the author of this Gospel believed Jesus to be a God. I believe all this should answer your questions!