Kinetic facades provide numerous advantages, such as improving the energy efficiency in buildings, effective control of daylight and natural ventilation, and the assurance of human comfort within indoor spaces. Either in the process of designing or programming the active control systems for kinetic facades, addressing the complicated nature of indoor climate necessitates advanced models that aid in determining optimal operations. However, the status quo of multi-objective (MOO) optimization in kinetic facade performance remains largely unexplored in the existing literature. This study delves into the trends in MOO methods and their broad applications through a scientific mapping and quantitative review process. The goal is to investigate the kinetic facade designers' contributions to expanding the application of computational MOOs. The findings indicate that researchers focused on kinetic facades have played a limited role in extending the MOO applications. This review paper is significant as it explores a less-explored facet of knowledge related to building design optimization, aiming to inspire researchers to stay abreast of evolving trends and integrate recent computational innovations into their facade designs.