Gluon fusion, the dominant mode of Higgs boson production at the LHC, is characterised by large amounts of initial-state gluon radiation and correspondingly large higher-order contributions to the inclusive and differential cross sections. In the inclusive Higgs cross section, coefficients of higher orders grow rapidly, leading to uncertainties outside the range of traditional estimates. In differential cross sections, there are large logarithmic enhancements of higher-order terms in important regions of phase space, which can however be summed to all orders. I will discuss the best current Standard Model estimates of the inclusive cross section, the Higgs transverse momentum distribution and the distribution of radiated transverse energy. I will also compare and contrast gluon fusion with the next most important production mode, vector boson fusion. Distinguishing between these processes is important for checking the Higgs couplings to fermions and bosons.