A remarkable level of precision has been reached in the measurement of the properties of the Higgs boson at the LHC. This has fueled the interest in improving theoretical predictions for Higgs-related processes. In this talk I will take as example the process gg->ZZ, which is important for the indirect determination of the Higgs width, and I will discuss the calculation of the virtual QCD corrections at next-to-leading order. I'll show how the technical challenge posed by two-loop box integrals with massive internal lines can be addressed using an expansion of the amplitude in terms of a small transverse momentum. This analytic approximation can be merged with a complementary expansion in the high-energy limit, allowing for an efficient evaluation of the two-loop amplitude over the complete phase space. Finally, I'll comment on the use of similar expansions for the process gg->HH.