That we should even be talking about Luke-Acts or “Luke and Acts” is an open question in contemporary scholarship. It has become common in Luke-Acts studies to discuss several potential ways in which Luke and Acts can be read together. Following the outline of Pervo and Parsons (Rethinking the Unity of Luke and Acts), there are five factors to consider when discussing the unity of Luke and Acts.
First, authorial unity is almost universally accepted. Recently, however, Patricia Walters challenged this consensus in her 2009 monograph The Assumed Authorial Unity of Luke and Acts. She argued the summary statements in Luke and Acts indicate two different authors. Walters’s study has been frequently reviewed so it is not necessary to fully examine her argument here. I agree with the common criticism her sample texts are too small to be significant. Although Walters’s study has convinced few, it is at least possible Luke and Acts come from two different authors.
Second, literary unity refers to reading Luke and Acts together as a unit. Since Cadbury’s The Making of Luke-Acts in 1939, it has become customary to refer to Luke and Acts with a hyphen, or perhaps a slash, as if to say there is a single book with two parts. An analogy might be Josephus’s multi-volume Antiquities of the Jews or The Jewish War. In both cases there are themes and interests running through all of the books in the series and it is quite clear Josephus intended his Antiquities as a unit. In fact, there are no real segues in Antiquities at the beginning of a new book. In the case of Luke-Acts, there is an intentional allusion to the first book at the beginning of Acts and many have observed some literary connections between the end of Luke and the beginnings of Acts. Luke Timothy Johnson focuses on the literary aspects of Luke-Acts in his commentary, the most significant to him are similar miracles by Jesus, Peter and Paul. In fact, these are the only parallels most commentators notice between Luke and Acts. Johnson does state that “Acts should be read in the light of the Gospel: just as Luke’s first volume can best be understood in the light of these literary patterns established in the first section of Acts” (13).
Third, it is possible to accept a single author but reject literary unity based on the genre of each book. Mikeal Parson and Richard Pervo issued just this challenge to the consensus view in their 1993 monograph Rethinking the Unity of Luke and Acts (Fortress 1992). Parsons and Pervo do not deny the same author wrote both books, but they question whether the genre of Luke is the same as Acts. If it differs, were the books intended to be read as a unit? For Pervo, “The unities of Luke and Acts are questions to be pursued rather than presuppositions to be exploited” (Pervo, Acts, 20)
Fourth, unity may refer to the purpose of the two books. Did a single author intended a single, overarching purpose for a unified two volume work? For Johnson, “As a whole, Luke-Acts should be read as an Apology in the form of a historical narrative” (Acts, 7). Yet the purpose of Luke may be narrowed to Jesus and his death on the Cross, while Acts concerns the spread of the message of the Cross throughout the Roman world. These may be related purposes, but they are not necessarily the same.
Fifth, even if some or all of these other unities prove true, it is possible to challenge the unity of Luke-Acts by using a relatively new approach, Reception History. Kavin Rowe, for example, argues no one in the early church ever read a book called “Luke-Acts” as a single unit. Canonically, the two were always separated and it was not until modern scholarship that anyone thought to read them as a unit. Building on the work of Andrew Gregory, Rowe examines Gregory’s two exceptions which appear to read Luke and Acts together, and concludes these are not true exceptions at all. Both Irenaeus and the Muratorian Canon focus on the authority of the Gospel of Luke rather than Acts. In fact, for Rowe, there is no evidence Luke and Acts were ever circulated as a unit. Acts sometimes introduced the Pauline or Catholic epistles, but no manuscript collected Luke and Acts as a two-part book.
Nevertheless I suggest there are a number of intra-textual links between Luke and Acts that support a literary unity between the two books. The introduction to both books certain link them together as a two-part work. A real problem for reading the two books together (whether hyphenated or slashed) is that there is no evidence the two books were ever considered together in the early church. In every New Testament canonical collection, Luke is placed with the gospels, Acts is set off on its own (sometimes as an introduction to the Pauline collection, but not always). Even if Luke intended them to be read together, until the modern era, no one read a book called “Luke-Acts.”
On Acts and Reception history, see C. Kavin Rowe, “History, Hermeneutics and the Unity of Luke-Acts,” JSNT 28 (2005): 131-157; Luke Timothy Johnson, “Literary Criticism of Luke-Acts: Is Reception-History Pertinent?” JSNT 28 (2005): 159-162; Markus Bockmuehl, “Why Not Let Acts Be Acts?: In Conversation With C. Kavin Rowe.” JSNT 28 (2005): 163-166; Andrew Gregory, “The Reception of Luke and Acts and the Unity of Luke-Acts.” JSNT 29 (2007): 459-472.  Andrew F. Gregory, The Reception of Luke and Acts in the Period before Irenaeus: Looking for Luke in the Second Century (WUNT 2/169; Tübingen: Mohr Siebeck, 2003). Gregory responds to Rowe’s use of this work in “The Reception of Luke and Acts and the Unity of Luke-Acts,” JSNT 29 (2007): 459-72.