Q:

Who Were Mark and Luke?

From Luke 6:13–16 (NIV):

When morning came, he called his disciples to him and chose twelve of
  them, whom he also designated apostles: Simon (whom he named Peter),
  his brother Andrew, James, John, Philip, Bartholomew, Matthew,
  Thomas, James son of Alphaeus, Simon who was called the Zealot, Judas
  son of James, and Judas Iscariot, who became a traitor.

John and Matthew were included, but the remaining two authors of the Gospel – Mark and Luke – were not.  Why is this, and how did they come to know Jesus so closely as to later write his Gospel?

A:

Historically, Mark is seen as one of Peter's disciples.  The historian Papias in the 2nd Century refers to him as such.  Likewise, the evidence in the narrative, for example, indicates that Peter was a significant source for most of the material, and most theologians accept Mark as "Peter's" Gospel.  Also, its seeming indication that the Temple is still standing marks it as an early Gospel.
Luke was Paul's travelling companion.  From very early on, this is what the church has taught. Luke and Acts were clearly written by the same individual (See Acts 1), and Luke is the traditional author. 

A:

Luke 10:1 (NIV)
After this the Lord appointed seventy-two[a] others and sent them two by
   two ahead of him to every town and place where he was about to go.
 [a] Some manuscripts seventy; also in verse 17 

Jesus did not have only Twelve disciples. There were other Seventy or Seventy-two disciples that Jesus appointed to preach the Gospel.
According to Wikipedia, it is possible that Mark and Luke were included in the Seventy disciples (check the list of Seventy disciples). If this is the case, it is no wonder that Mark and Luke could write the Story of Jesus accurately. 

A:

From the second century, Mark and Luke came to be seen as the probable authors of two of the New Testament gospels, as were Matthew and John. The fourth century Church historian Eusebius, in Ecclesiastical History,III, credits Papias, a bishop from the early second century, with naming Mark as a Gospel writer:

Ecclesiastical History,III, 39.15: Mark became Peter's interpreter and wrote accurately all that he remembered, not, indeed, in order, of the things said or done by the Lord. For he had not heard the Lord, nor had he followed him, but later on, as I said, he followed Peter, who used to give teaching as necessity demanded but not making as it were, an arrangement of the Lord's oracles, so that Mark did nothing wrong in thus writing down single points as he remembered them.  For to one thing he gave attention, to leave out nothing of what he had heard and to make no false statements in them. 

Since Eusebius was a sometimes unreliable historian, we can not be certain whether Eusebius is reliable in attributing to Papias the claim that Mark was a gospel author, and Rex Wyler point out, in The Jesus Sayings, page 119, we possess no other evidence that supports this conjecture. The Mark to whom Eusebius refers had been mentioned by Paul as one of his fellow workers in his Epistle to Philemon (chapter 24) and also mentioned in Acts of the Apostles. Then, in the first epistle of Peter (l Peter 5:13), a pseudonymous document from the late first century or early second century, Mark is mentioned as Peter's son. It is on the basis of these reports that Papias is likely to have seen Mark as a possible gospel author.
Raymond E. Brown says in An Introduction to the New Testament, page 267, that by the latter half of the second century, the gospel now known as Luke was being attributed to Luke the companion whom Paul mentions in Philemon 24, and who is also mentioned under Paul's name in Colossians 4:14 and 2 Timothy 4:11.
Bart D. Ehrman says in Forged, page 207, Luke was established as the author of the gospel that now bears his name, and therefore of Acts, by a process of elimination. The anonymous author was someone who  especially concerned with the Gentile mission of the early church and who is particularly interested in showing that Gentiles do not have to become Jews in order to be Christian, so it is sensible to conclude that this person was probably himself a Gentile. By his occasional use of “we”, the author is claiming to be a travelling companion of Paul.
There are three persons in Colossians who were Gentile companions of Paul: Epaphras, Demas, and Luke.  Of these, Ehrman says it seems unlikely that Demas could be the author, since we learn elsewhere that Demas "abandoned" Paul (2 Timothy 4:10). Epaphras appears to have been known as the founder of the church in Colossae (Colossians 1:5-7), a church that is never mentioned in Acts, so it would be odd if its founder were the author. This leaves one candidate as the author of Luke and Acts of the Apostles: Luke the Gentile physician.

