With the growing trend towards preserving global architectural heritage, the adaptive reuse of built heritage buildings is becoming increasingly popular; as commentators have noted, this popularity can in part be attributed to the economic, cultural, and social benefits they provide to urban communities. In considering adaptive reuse, urban developers and planners seek to reach an equilibrium in the battle between time and space. Both academically and practically, the adaptive reuse of heritage buildings requires compatible, appropriate, and scientific means for assessing built heritage assets; however, currently, research in this area is still relatively meagre. To address this gap, this paper investigates research frameworks, methodologies, and assessment methods that concern the adaptive reuse of architectural heritage. In this paper, we examine the current literature on the paradigms for applying mixed methodologies: the multi-criteria decision model (MCDM) and the preference measurement model (PMM). Specifically, in examining the extant literature, we explore the ways in which these methods are discussed, compared, and evaluated, and the positive functions of these methods are also highlighted. In addition, this review examines a range of cases to better clarify the research frameworks, methodologies, and assessment methods used in the study of the adaptive reuse of architectural heritage.