In the last few years, studies on modern architecture in Latin America have intensified to the point in which it may be said that the first requirement for all historiography has been completed: that of inventory. As a collective effort it is now necessary to undertake the interpretation of the said inventory in studies involving long periods in the totality of Latin America. Following Juan Pablo Bonta’s invitation to exercise didactic architectural games, the text presents three different criteria and interpretations regarding the process of modern Latin American architecture as synthetic characterization of relevant built works, with a brief criticism of each one of them.