Despite the fact that importing and exporting are extremely rare firm activities, economists generally devote little attention to the role of firms when discussing international trade. This paper summarizes key differences between trading and non-trading firms, demonstrates how these differences present a challenge to standard trade models and shows how recent "heterogeneous-firm" models of international trade address these challenges. We then make use of transaction-level U.S. trade data to introduce a number of new stylized facts about firms and trade. These facts reveal that the extensive margins of trade--that is, the number of products firms trade as well as the number of countries with which they trade--are central to understanding the well-known role of distance in dampening aggregate trade flows.