We give an overview of the present status of knowledge of the production of J/ψ, ψ′ and Υ in high-energy hadron collisions. We first present two early models, namely the ColourSinglet Model (CSM) and the Colour-Evaporation Model (CEM). The first is the natural application of pQCD to quarkonium production and has been shown to fail dramatically to describe experimental data, the second is its ph...