Decay constants and sigma terms from the lattice

Thanks to the recent developments both in our understanding of lattice simulations and in computer power, accurate predictions can now be made in nonperturbative QCD, with all sources of error under control. I review recent results of the Budapest-Marseille-Wuppertal lattice collaboration. The first concern the pion and kaon leptonic decay constants, which can be combined with experiment to determine CKM matrix elements and check the unitarity of this matrix's first row. The second pertain to the nucleon sigma terms, which are important for calculating the sensitivity to dark matter of direct search experiments. For the latter, preliminary results based on a subset of our new dataset will be presented. I will emphasize how we are able to control systematic errors in these calculations.