Not the factorizations you're thinking of! A 1-factorization of a graph is a partition of its edges into perfect matchings. In this talk I hope to share some of the many questions about 1-factorizations that I find interesting, explain how I came to care about a rather obscure fact, and prove it. Along the way we will draw some pretty pictures, of course. This talk should be totally accessible to anyone who has ever heard of graphs, and is based on collaboration with Michael Orrison and Rohan Chauhan.