We revisit and rehabilitate linear models of interactions in binary outcomes. Building on Heckman and MaCurdy (1985), we characterize when these models are statistically well defined. We then characterize and assess their game-theoretic microfoundations. We show that linear models of interactions admit sensible microfoundations under incomplete information and independence, but unconventional ones under complete information. We propose two simple estimators and revisit the empirical analyses of teenage smoking and peer effects of Lee, Li, and Lin (2014) and of entry into airline markets of Ciliberto and Tamer (2009). Our reanalyses highlight the main advantages of the linear framework and suggest that the estimations in these two studies suffer from endogeneity problems.