Equilibrium models are one of the pillars of Economics. This proposal focuses on methodological and empirical studies of estimable game theoretic and social interactions models where observed outcomes are assumed to be determined in equilibrium. Ignoring this simultaneity in estimation and inference is likely to mislead conclusions and produce flawed counterfactual analyses.One pervasive feature in many interaction models is the existence of multiple solutions for various payoff configurations, and this is an aspect that carries over to estimable versions of such systems. Overlooking this possibility or assuming an uninformed equilibrium selection process potentially opens the door to severe misspecifications and erroneous conclusions. Another notable complication in the analysis of interaction models is computability: with a large number of players and sizeable set of outcomes and/or states, the search for an equilibrium solution can be daunting.The research projects contemplated in this proposal address one or both of these aspects in various different settings. Those projects contain methodological and substantive contributions. The work involves advances in the econometric analysis (identification and estimation) of interaction models and empirical implementation of the devised methodologies to questions of interest. Given the widespread and increasing use of such econometric models, the projects contemplated here will have a fundamental impact.I divide the projects into three main subtopics:1) Identification and inference in games with multiple equilibria,2) Social interactions and network models,3) Dynamic interaction models.