I will discuss modern approaches to the calculation of multi-scale two-loop integrals. These techniques have recently been used to compute the complete set of integrals required for five-point scattering processes with a single massive external leg at two loops. I will present the techniques we used in this calculation, and comment on the analytic structure of these integrals. Finally, having in mind phenomenological applications, I will discuss how to construct a basis of so-called pentagon functions for this set of integrals.