We present a comprehensive QCD-based model for the x f and nuclear dependences of heavy quarkonium production in photon-, hadron-, and nuclear-induced collisions. The calculated x f dependence reflects both leading-twist QCD fusion subprocesses and higher-twist intrinsic heavy-quark components of the hadron wavefunction. A-dependent effects due to final-state absorption, interactions with comovers, shadowing of parton distributions, and intrinsic heavy-quark components are identified. The model is compared with data for J/ ψ, ψ 1 and ϒ production in pion,proton, and nucleus-nucleus collisions.