Inspired by work of Rogers in the classical geometry of numbers, we'll describe how to obtain variance bounds for classical geometric counting problems in the settings of translation surfaces and hyperbolic surfaces, and give some applications to understanding correlations between special trajectories on these types of surfaces. Parts of this will be joint work with Y. Cheung and H. Masur; S. Fairchild and H. Masur; and F. Arana-Herrera, and all of this has been inspired by joint work with G. Margulis.