With 5.9 binary black hole mergers and 1 binary neutron star merger announced so far, the Advanced LIGO and Virgo detectors have started their census of the local(ish) compact binary population. With detection rates as high as one per week in the next observing run, and one per day in the coming years, we will quickly accumulate the statistics necessary to constrain the physics relevant to binary formation. I will present some the techniques being developed to make these inferences, what we have learned so far, and what we might learn in the near future.