The traditional view of trade - in final products that are considered packages of domestic factor inputs - has been upset by the emergence of trade in intermediate inputs. The labeling of products as "made in China" (or whichever country) is little informative when the assembled parts have been produced elsewhere. Only this century three sets of indicators have been launched to measure the international fragmentation of products - following the vertical specialization approach, the global value chain approach and the value-added exports approach. The differences are introduced using a stylized global production network of five countries, the respective policy measures are identified and the input-output-based formulas are presented. Next the testing of trade theories is discussed, starting with the Leontief paradox: the classic rejection of the neoclassical Heckscher-Ohlin theory. Various refinements in the literature, accounting for technology differences, international fragmentation and other variations, are reviewed. The author makes tantalizing suggestions for further research, including the modeling of international production networks and the decoupling of primary inputs (e.g., greenhouse gas emissions) from gross outputs.