Luke was the most prolific author of the New Testament. Together the Gospel of Luke and Acts of the Apostles comprise 27.5% of the NT, which is more than Paul’s letters. We do not know much about Luke, but there is a bit that we do.
One who wrote with artistry
Luke is an artist. His Gospel account is known for his literary quality. He often paired stories together, usually containing a woman as the central figure in one and a man as the central figure in the other.
His artistry in composing his account can even be seen at the level of the sentence. At times, he will pair two terms together that in English sound like a hodgepodge, but in Greek roll off your tongue with rhythm and poetry. An example is in Luke 5:29-32 (NIV):
Then Levi held a great banquet for Jesus at his house, and a large crowd of tax collectors and others were eating with them. But the Pharisees and the teachers of the law who belonged to their sect complained to his disciples, “Why do you eat and drink with tax collectors and sinners?”
Jesus answered them, “It is not the healthy who need a doctor, but the sick. I have not come to call the righteous, but sinners to repentance.”
This short passage has six word-pairs (tax collectors/others, Pharisees/teachers of the law, eat/drink, tax collectors/sinners, healthy/sick, righteous/sinners). The English pairs show no obvious links to one another; the Greek pairs show blatant grammatical similarities in their endings that would allow them to roll off the tongue as if they were rhyming. An example is eat/drink, which in Greek is ἐσθίετε/πίνετε (esthiete/pinete) or tax collectors/sinners, which in Greek is τελωνῶν/ἁμαρτωλῶν (telonon/hamartolon).
One adept with Greek
Luke writes in excellent Greek. His facility with Greek is the best among the Gospel writers and among the best in all of the New Testament, which places him in a certain social location: educated, likely in the Hellenistic world. He has a wide range of vocabulary, using words not used by any other writer (these are called hapax legomenon, which means “being said once”) in the rest of the New Testament, such as perispao, glossed as “distracted” and used to describe Martha in Luke 10.
Together with the fact that his Gospel does not contain the Hebraisms of Matthew and John, that he does not seem to have skills in Hebrew or Aramaic, but that he does seem to be quite familiar with the Septuagint (LXX), the Greek translation of the Hebrew Bible/Old Testament, it seems that Luke is either a diaspora Jew raised in a Greek context, or a Gentile God-fearer who attended a synagogue.
Luke was writing to Theophilus. Theophilus is a Greek name (meaning “lover of God”) and indicates most likely that he was a wealthy Greek man, perhaps a God-fearer, serving as Luke’s patron. Luke seems to indicate a patron-client relationship by addressing Theophilus as kratistos in Luke 1:3, meaning honorable or noble, most often used to address men of prominent rank. Likely, Theophilus paid for the expenses involved in doing first-hand research and writing of this careful and orderly account. Luke is thus deep and comfortable in Greek circles.
One knowledgeable about medicine
In his second book–Acts of the Apostles–Luke switches from the third person to the first person, indicating that he was among Paul and his band during some of the travel period. In Col. 4:14 Paul mentions that his dear friend Luke, the doctor, gives his greetings, indicating that Luke was with him. That Luke was a physician is backed up by other hapax legomona in his Gospel account which refer to medical terms, such as hudropikos in Luke 14:2 (glossed as ‘abnormal swelling’ in the NIV) or thromboi in Luke 22:44 (glossed as ‘drops’ [of blood]).
One attentive to the Spirit
Another reason for thinking that Luke was a companion of Paul is his frequent mention of the Holy Spirit. While the other three Gospel writers mention the Holy Spirit four to five times each, Luke mentions the Spirit thirteen times in his Gospel account, and 42 times in Acts. It makes sense that upon seeing the acts of the Spirit often during his time with Paul, that Luke would be more likely to recognize the activity of the Spirit as he wrote his Gospel account.