This paper surveys the recent body of work in economics on the importance of global value chains (GVCs) in shaping international trade flows and multinational activity. On the empirical front, we begin reviewing several variants of the "macro approach" to measuring the relevance of global production sharing in the world economy, and we also offer a critical evaluation of the country- and industry-level datasets (or World Input Output Tables) that have been used to date. We next discuss the advantages and disadvantages of a burgeoning alternative "micro approach" that has instead employed firm-level datasets to document the ways in which firms have sliced up their value chains across countries. On the theoretical front, we propose an analogous dissection of the literature. First, we review a vast body of work developing country- and industry-level quantitative frameworks that are easily calibrated with World Input Output Tables, and that open the door for counterfactual exercises with minimal demands on estimation. Second, we overview micro-level frameworks that have treated firms rather than countries or industries as the relevant unit of analysis, and that have unveiled a number of distinctive mechanisms by which GVCs shape the determinants and consequences of international trade flows in ways distinct from traditional models of international trade. We close this survey with a discussion of a still infant literature on the desirability and effects of trade policy in a world of GVCs.