We review some of the major progress in the accurate calculation of the cross section for the production of a charged Higgs boson in a generic two-Higgs double model, by focussing on the high-mass region, for which new calculations have been made available in the past few years, both at the level of total and of differential cross sections. Furthermore, we illustrate some recent progress in the calculation of the total cross section for a charged Higgs boson with mass in the intermediate range $m_{H^\pm}\sim m_t$, including top-resonant contributions.