In the first part of the talk, I will discuss the distribution of rationality fields of modular forms. Maeda's conjecture predicts they are as large as possible in level 1. In higher level, this is not quite true but I will discuss how close this is to being true. In particular, I will present conjectures joint with Alex Cowan on the frequency of a given rationality field. In the second part of the talk, I will discuss joint work with Alex Cowan and Sam Frengley on constructing families of genus 2 curves with real multiplication over Q. One can use these families to give lower bounds on the number of modular forms with fixed quadratic rationality field.