Gospel of Luke
The Gospel of Luke is the third (traditionally) of the four canonical gospels of the New Testament and also the longest. It is also considered one of the three synoptic gospels. It was likely written sometime between 75-100 CE.
Historians virtually all agree that authorship of Luke took place before c. 150 due to the presence of widespread quotes and references to Luke in other early manuscripts from the latter half of the second century. Furthermore, the earliest church fathers, as well as the majority of historians through time up to the present, generally still date Luke to around c. 75-100. The lower bound to this range arose primarily due to the textual parallels in Luke that indicate he used Mark as a source and also the general sense that the details about the Temple's destruction mentioned in Luke 21:5-30 (where Jesus merely foretells of the coming destruction of the Temple) are sufficiently strong to indicate Luke was probably a witness to the destruction in c. 70, or working from a source written by a witness. The upper bound arose out of the assumption that the heretical Gospel of Marcion, which was likely formulated and written in the early half of the 2nd century, seemed undeniably based upon Luke, though no direct reference to Luke was ever made in the Gospel of Marcion.
However, one revisionist view still persists today among a minority of scholars, which states this situation might be the reverse -- that Luke may be based on Marcion. This alternative theory proposed that Marcion may have used the same primary synoptic source that Luke used (that is, the Gospels of Mark) rather than Luke itself. Furthermore, the undeniable parallels that exist between Luke and Marcion thus might have arisen out of Luke using Marcion (as well as Mark) -- rather than the other way around -- as an attempt by the author of Luke to "undue" the damage created by the heretical Gospel of Marcion that was competing strongly with church doctrine during the middle of the second century. If the latter hypothesis is true, the date of authorship for Luke would likely closer to c. 150, when the Gospel of Marcion was in wide distribution.
A minority of historians also assert that Luke may have been written before c. 75. These views are based primarily upon negative evidence. Other than the reference to the premonition mentioned above, the author of Luke failed to mention anything that occurred historically after c. 67 -- such as the deaths of prominent Christians, like Jesus' brother James or Luke's long time friend, Paul, or Peter, or any of the persecutions by Nero of Christian leadership that all took place after c. 64 (according to Tacitus). In addition, Luke also does not mention anything about the destruction of Jerusalem that occurred at this same time as the Temple destruction in c. 70. Of course, such omissions might also indicate that Luke was written long after these events took place, rather than before, and if written as a counter-balancing view of another work (such as the Gospel of Marcion) such circumstances could easily explain why such events do not appear in Luke. There is no evidence that the Gospels ever attempted to record historical events, so omission of significant events such as these is hardly a strong rationale to use for the dating of authorship.
In any case, the oldest existing manuscript today of the Gospel of Luke dates to around C. 200.
Textual Similarities & Scriptural Parallels
Text analyses has strong evidence to support the theory that whoever wrote the Gospel of Luke, likely also authored the Book of Acts in the New Testament too.
The historical community is near equally divided over who likely was the actual author of Luke. Traditionally (and unanimously among religiously practicing scholars) the physician, and early Christian writer known as Luke the Evangelist, who was the primary companion to Paul during his travels, is attributed with authorship of this gospel. There is some sparse and weak evidence to support this hypothesis. Foremost, of the two earliest manuscripts we have, one has an attribution "According to Luke" actually written in it (which is rare in ancient Christian manuscripts, especially when they are written by anonymous authors). Another piece of circumstantial evidence points to how the author refers to Paul in his writings by the first person plural, which indicates the author was likely a companion to Paul. Other scholars have felt the use of language in both Luke and Acts (which have common authorship) connotes medical terminology, which hints that the author likely had medical training. Luke the Evangelist has been widely cited in several ancient sources, as being a physician.
Due to the minimal nature of this evidence, and given the tendency of early Christians to forge such documents on a regular basis and attribute them to famous Christian leaders of their day, many historians still doubt this attribution.