Qualitative spatial and temporal reasoning (QSTR) is concerned with symbolic knowledge representation, typically over infinite domains. The motivations for employing QSTR techniques include exploiting computational properties that allow efficient reasoning to capture human cognitive concepts in a computational framework. The notion of a qualitative calculus is one of the most prominent QSTR formalisms. This article presents the first overview of all qualitative calculi developed to date and their computational properties, together with generalized definitions of the fundamental concepts and methods that now encompass all existing calculi. Moreover, we provide a classification of calculi according to their algebraic properties.