Linear models, such as force constant (FC) and cluster expansions, play a key role in physics and materials science. In this talk, I will discuss methods for the systematic construction of such models as well as their application in various scenarios. Special emphasis will be put on the hiphive and icet software packages that we have developed over course of several years for this purpose. In this context, I will discuss the efficacy and efficiency of several state-of-the-art regression and feature selection methods, including methods routed in Bayesian statistics such as automatic relevance detection regression.