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What are the formation channels of merging black holes and neutron stars? The first two observing runs of Advanced LIGO and Virgo give us invaluable insights to address this question, but a new approach to theoretical models is required, in order to match the challenges posed by the new data. In my talk, I present a new model to study the progenitor stars of merging systems, by considering both dynamical and isolated binary evolution within a cosmological framework. I discuss the impact of stellar winds, core-collapse and pair instability supernovae on the formation of compact remnants in both isolated and dynamically formed binaries. Finally, I show that dynamical processes, such as dynamical exchanges and hardening, leave a clear imprint on the demography of merging systems.