In this talk we will outline the proof of homological stability for scissors automorphism groups and highlight a number of consequences and related results. These include plus and group completion constructions for assembler K-theory, interpreting higher K-theory in terms of automorphism groups, and homology calculations for some scissors automorphism groups. In this framework, we can compute group homology of the interval exchange group and generalizations of Thompson's group V. The content of the talk is joint work with Kupers, Malkiewich, Miller, and Sroka.