Over the last six years, the LIGO and Virgo gravitational wave detectors have revolutionized gravitational wave astronomy by discovering the first compact binary mergers. There is much to learn about how these systems form in nature, and these discoveries have allowed to start characterizing the astrophysical population of binary black holes. Many layers of data processing are needed in the path from raw gravitational wave data to inference of astrophysical implications. In this thesis, I worked on algorithms to search for signals from compact binary mergers, estimating their parameters and analyzing them collectively to infer properties of the astrophysical population, aimed at key questions in gravitational wave astronomy: What is the rate of binary mergers in the Universe? What is the distribution of masses and spins? What is the formation mechanism of merging binary black holes? I construct a bank of waveform templates suitable for searching compact binary mergers in gravitational wave data through matched-filtering. The resulting bank is defined on a geometric space, whose notion of distance between waveforms naturally corresponds to their response mismatch. Beyond aiding intuition, this feature enables optimal placement of templates, dynamical refinement of the search, and powerful and robust signal quality tests. Using this template bank, my collaborators and I carried out a search for binary black holes in public LIGO-Virgo data, confirming previous detections and identifying nine new events. I compute the likelihood function for the parameters of the individual sources, such as black hole masses and spins. I derive a framework to combine these pieces of information into a likelihood for the collective distribution of these parameters, that accounts for measurement uncertainties, selection effects and statistical significance of the events. With this, I test and constrain phenomenological models for the distribution of binary black hole masses, spins, merger rates and cosmological evolution. I find that the mass distribution features a steep drop around 40 solar masses, as predicted by the pair-instability supernova mechanism; but also features an extended tail to higher masses. The distribution of spin orientations is anisotropic, disfavoring dynamical formation channels as the only pathway for merging binary black holes.