This paper discusses the estimation and interpretation of gravity equations for bilateral trade. Gravity equations are a model of bilateral interactions where size and distance effects enter multiplicatively. They have been used as a workhorse for analyzing the determinants of bilateral trade flows for 50 years since being introduced by Tinbergen (1962). Gravity equations are often referred to as examples of "social physics," the relatively few law-like empirical regularities that characterize social interactions. Over the last decade, concentrated efforts of trade theorists have established that gravity equations emerge from mainstream modeling frameworks in economics and should no longer be thought of as deriving from some murky analogy with Newtonian physics. Meanwhile empirical work—guided in varying degrees by the new theory—has proceeded to lay down a raft of stylized facts about the determinants of bilateral trade. As a result of recent modelling, we now know that gravity estimates can be combined with trade policy experiments to calculate implied welfare changes. This chapter focuses on the estimation and interpretation of gravity equations for bilateral trade. This necessarily involves a careful consideration of the theoretical underpinnings since it has become clear that naive approaches to estimation lead to biased and frequently misinterpreted results. There are now several theory-consistent estimation methods and we argue against sole reliance on any one method and instead advocate a toolkit approach. One estimator may be preferred for certain types of data or research questions but more often the methods should be used in concert to establish robustness. In recent years, estimation has become just a first step before a deeper analysis of the implications of the results, notably in terms of welfare. We try to facilitate diffusion of best-practice methods by illustrating their application in a step-by-step cookbook mode of exposition. The paper discusses the microfoundations for gravity equations, including three definitions of the gravity equation. The first definition includes the set of models that yield bilateral trade equations that can be expressed as X_{ni}=G S_i M_n phi_{ni}. The second definition includes the subset of general gravity models in which bilateral trade is given by X_{ni}=S_i M_n phi_{ni}, where S_i and M_n are defined as the "capabilities" of the exporter and the characteristics of the destination market. The third definition includes naive gravity equations that express bilateral trade as X_{ni}=G Y_i^a Y_n^b phi_{ni}. The paper also discusses the assumptions underlying structural gravity, including the spatial allocation of expenditure for the importer and market-clearing for the exporter. It then considers the main variants of gravity for trade, including demand-side and supply-side derivations. The paper concludes with a discussion of the frontiers of gravity research, including the errors in gravity equations, the causes and consequences of zeros, and firm-level gravity, extensive and intensive margins.This paper discusses the estimation and interpretation of gravity equations for bilateral trade. Gravity equations are a model of bilateral interactions where size and distance effects enter multiplicatively. They have been used as a workhorse for analyzing the determinants of bilateral trade flows for 50 years since being introduced by Tinbergen (1962). Gravity equations are often referred to as examples of "social physics," the relatively few law-like empirical regularities that characterize social interactions. Over the last decade, concentrated efforts of trade theorists have established that gravity equations emerge from mainstream modeling frameworks in economics and should no longer be thought of as deriving from some murky analogy with Newtonian physics. Meanwhile empirical work—guided in varying degrees by the new theory—has proceeded to lay down a raft of stylized facts about the determinants of bilateral trade. As a result of recent modelling, we now know that gravity estimates can be combined with trade policy experiments to calculate implied welfare changes. This chapter focuses on the estimation and interpretation of gravity equations for bilateral trade. This necessarily involves a careful consideration of the theoretical underpinnings since it has become clear that naive approaches to estimation lead to biased and frequently misinterpreted results. There are now several theory-consistent estimation methods and we argue against sole reliance on any one method and instead advocate a toolkit approach. One estimator may be preferred for certain types of data or research questions but more often the methods should be used in concert to establish robustness. In recent years, estimation has become just a first step before a deeper analysis of the implications of the results, notably in terms of welfare. We try to facilitate diffusion of best-practice methods by illustrating their application in a step-by-step cookbook mode of exposition. The paper discusses the microfoundations for gravity equations, including three definitions of the gravity equation. The first definition includes the set of models that yield bilateral trade equations that can be expressed as X_{ni}=G S_i M_n phi_{ni}. The second definition includes the subset of general gravity models in which bilateral trade is given by X_{ni}=S_i M_n phi_{ni}, where S_i and M_n are defined as the "capabilities" of the exporter and the characteristics of the destination market. The third definition includes naive gravity equations that express bilateral trade as X_{ni}=G Y_i^a Y_n^b phi_{ni}. The paper also discusses the assumptions underlying structural gravity, including the spatial allocation of expenditure for the importer and market-clearing for the exporter. It then considers the main variants of gravity for trade, including demand-side and supply-side derivations. The paper concludes with a discussion of the frontiers of gravity research, including the errors in gravity equations, the causes and consequences of zeros, and firm-level gravity, extensive and intensive margins.