We present the Monte Carlo event generator WINHAC for Drell–Yan processes in proton–proton, proton–antiproton, proton–ion and ion–ion collisions. It features multiphoton radiation within the Yennie–Frautschi–Suura exclusive exponentiation scheme with electroweak corrections for the charged-current processes and multiphoton radiation generated by PHOTOS for neutral-current ones. For the initial-state QCD/QED parton shower and hadronisation, it is interfaced with PYTHIA. It includes several options, e.g. for the polarized W-boson production, generation of weighted/unweighted events, etc. WINHAC was cross-checked numerically at the per-mille level with independent Monte Carlo programs, such as HORACE and SANC. It has been used as a basic tool for developing and testing some new methods of precise measurements of the Standard Model parameters at the LHC, in particular the W-boson mass. Recently, it has been applied to simulations of the double Drell–Yan processes resulting from double-parton scattering, in order to assess their influence on the Higgs-boson detection at the LHC in its ZZ and decay channels.