The historiography dedicated to the study of Mudejar art in Latin America and the Canary Islands has evolved over the years. The Spanish mudejaristas were the first to study the phenomenon, extrapolating the knowledge, theories and terminology developed in the study of Iberian cases to those observed in colonized territories. This has led to misapplications that do not respond to the particular needs of this cultural legacy. In this article, we first review the state of the question in order to establish definitions and reformulate concepts such as Mudejar art, cultural survival, roots or tradition.