A deep understanding of the Higgs sector is one of the paramount aims of the LHC, and in particular of the Run II. The evidence of extra, possibly charged, Higgs bosons would be a clear sign of physics beyond the Standard Model. In this talk, I will review the recent progresses in simulating charged Higgs boson production at the LHC, mostly focusing on the case of a heavy charged Higgs boson in the two-Higgs-doublet-model. On top of its phenomenological importance, such a case is relevant also from the QCD point of view, as it can be described both in the four- and five-flavour scheme. I will compare results obtained in the two schemes, and show how a 4FS description should be preferred for fully-differential studies.