"High-energy observations of our Galaxy offer a good, albeit not complete, picture of the X-ray source populations, in particular the accreting binary sources. Recent ability to study accreting binaries in nearby galaxies has shown that we would be short-sighted if we restricted ourselves to our Galaxy or to a few nearby ones. I propose an ambitious project that involves a comprehensive study of all the galaxies within 10 Mpc for which we can study in detail their X-ray sources and stellar populations. The study will combine data from a unique suite of observatories (Chandra, XMM-Newton, HST, Spitzer) with state-of-the-art theoretical modelling of binary systems. I propose a novel approach that links the accreting binary populations to their parent stellar populations and surpasses any current studies of X-ray binary populations, both in scale and in scope, by: (a) combining methods and results from several different areas of astrophysics (compact objects, binary systems, stellar populations, galaxy evolution); (b) using data from almost the whole electromagnetic spectrum (infrared to X-ray bands); (c) identifying and studying the different sub-populations of accreting binaries; and (d) performing direct comparison between observations and theoretical predictions, over a broad parameter space. The project: (a) will answer the long-standing question of the formation efficiency of accreting binaries in different environments; and (b) will constrain their evolutionary paths. As by-products the project will provide eagerly awaited input to the fields of gravitational-wave sources, γ-ray bursts, and X-ray emitting galaxies at cosmological distances and it will produce a heritage multi-wavelength dataset and library of models for future studies of galaxies and accreting binaries."