In this talk I will discuss joint work with Ofir Gorodetsky and Sacha Mangerel in which we prove a central limit theorem for counts of squarefree integers in random short intervals. In fact closely related ideas allow one to prove a functional limit theorem – a path formed by counting squarefrees in a random short interval will tend to fractional Brownian motion, which I’ll attempt to explain. I hope to also discuss the generalization of squarefrees to B-frees which was first introduced by Erdős and analogous limit theorems for B-frees.