AM³ simulates lepto-hadronic interactions in astrophysical environments. It solves the time-dependent partial differential equations for the energy spectra of electrons, positrons, protons, neutrons, photons, neutrinos as well as charged secondaries (pions and muons), immersed in an isotropic magnetic field. The code accounts for the emission of photons and charged secondaries in electromagnetic and hadronic interactions feed back into the interaction rates in a time-dependent manner, therefore grasping non-linear effects including electromagnetic cascades. AM³ is computationally efficient, making it possible to scan vast source parameter scans and fit the observational data, and has been deployed to explain multi-wavelength observations from blazars, gamma-ray bursts and tidal disruption events.