The existence of an IRFP at strong coupling in four-dimensional gauge theories cannot be studied by the usual perturbative techniques. The nonperturbative regime of quantum field theories can be investigated from first principles by formulating the
theory on a Euclidean discretized spacetime. In this talk we summarize the techniques that have been developed for this purpose in recent years, and the latest results obtained in this area, with an emphasis on the necessity to control systematic errors. We conclude by discussing the potential impact of lattice results on the phenomenology of a strongly-interacting Higgs sector.