In this talk, I will discuss a trio of topics in theoretical astrophysics and cosmology. First, I will outline efforts to parametrize dark matter self-interactions in a scenario where there are multiple states participating and where inelastic transitions can occur. In particular, with an eye toward dwarf galaxies, I will show that the simplest inelastic model can efficiently ameliorate discrepancies between simulation and observation and can also provide a dark matter explanation for the 3.5 keV line observed in galaxies and in clusters. Second, I will discuss recent work in which I converted pulsar timing array constraints on gravitational waves into limits on the existence of supermassive black hole binaries in galaxies within 100 Mpc. I find that in certain host galaxies, one can already place upper limits on the binary mass ratio at the percent level using existing pulsar timing data. I show that it is possible to use this information to determine where it is most useful to search for new pulsars. Third, I will show results of a calculation of the non-Gaussian covariance of the matter power spectrum within the context of effective field theory. While this formalism is a promising way forward in understanding the nonlinearities of structure formation, the formalism requires measuring a single free parameter from N-body simulations. I show that current simulations of the covariance lack the needed accuracy for these purposes and I suggest alternative ways of measuring the effective parameter that would also require fewer simulations.