Atmospheric leptons are of continuous interest for several scientific communities. At low and intermediate energies, atmospheric neutrinos are the signal for studies of fundamental neutrino properties and at high energies, they constitute the background for the characterization of the features of the astrophysical neutrino flux. We have studied in depth the relation between observable inclusive lepton fluxes/ratios and hadronic interactions by using a novel numerical transport equation solver MCEq. It enables us to characterize, with an unprecedented precision, relevant particle interaction energies, important hadron species, and the secondary particle production phase-space in terms of typical accelerator observables. Based on our findings, we improved existing interaction models SIBYLL and DPMJET and created an efficient scheme to propagate correlated model uncertainties into derived lepton fluxes. We present state-of-the-art calculations of inclusive lepton fluxes and discuss possible directions towards reducing uncertainties below 10%.