Dr Kelly's research is primarily concerned with the function of tradition and the evolution of early Greek poetry from the 8th-6th centuries BC, and the development of different notions of 'text' during that period. He also writes on the relationship between Athenian tragedy and its society in the 5th century BC. He is currently working on an edition with commentary of the 23rd Book of Homer's Iliad.
- Ancient Greek epic poetry (8th-6th centuries BC), including Homer, Hesiod, the Homeric Hymns and the Epic cycle
- Athenian tragedy (5th century BC), including Aeschylus, Sophocles, Euripides
- Greek literature and culture (8th-5th centuries BC)