The Genesis view in Haydn’s oratorio "The Creation"

Image from Naxos

The Appendix of The Imagined Conflict lists these main positions for reconciling science and the Bible:

1. Young Earth creationism (YEC): Solar day theory
2. Old Earth creationism (OEC)
• Chaos-restitution interpretation 
• Gap theory
3. Progressive creationism: Day-age interpretation
4. Guided evolution
5. Planned evolution

There are in fact two more also listed: Deistic evolution and Atheistic evolution, but these views are not really about reconciliation as they more or less ignore the Bible as a source of knowledge.

Sometimes these five views are presented as a menu to choose from, but they have been developed in a dialogue with the development of science. They are best understood in a history of science context. 

This three first views above in particular are examples of concordism where the biblical order of creation is made to align with what science had found at the time. They were common before the theory of evolution. As an example Haydn’s oratorio The Creation from 1796 assumes a chaos-restitution interpretation where a gap of unspecified length is inserted in Genesis 1:1–2 betwen a much older chaos which was reordered during some recent six days.

The life of geologist and theologian William Buckland (1784–1856) is used in the book to illustrate how educated Christians moved from the gap theory view of old Earth creationism to the day-age view of progressive creationism. That was in the 1840s and 1850s when he was central in dating fossils like dinosaurs and combining this new knowledge with his reading of the Bible.

Views 4 and 5 build on a functional view of Genesis and/or a framework interpretation where the six days are understood thematically or logically rather than chronologically.

Read more in Chapter 4 The History of Life and the Universe, in Chapter 6 Evolution and Purpose, and the Appendix The Bible and Science.