Directional data (angular data), including circular and spherical data, have applications in many scientific fields such as ecology, medicine, biology, meteorology, finance, astronomy, geosciences, machine learning, and artificial intelligence. Modeling dependencies among such data has always faced fundamental challenges due to the periodic and nonlinear nature of angles. In recent decades, copulas have gained a prominent place in statistics as powerful tools for separating marginal structures from joint dependence. However, generalizing copulas to directional data—including circular–linear, circular–circular, and spherical–spherical copulas—has followed a complex and ongoing research path. In this paper, using a temporal–thematic approach, the historical development, construction methods, applications, dependence measures, estimation methods, and goodness-of-fit tests for directional copulas are reviewed.