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Electricity, heating, and cooling are the three main components constituting the tripod of energy consumption in residential, commercial, and public buildings all around the world. Their separate generation causes higher fuel consumption, at a time where energy demands and fuel costs are continuously rising. Combined cooling, heating, and power (CCHP) or trigeneration could be a solution for such challenge yielding an efficient, reliable, flexible, competitive, and less pollutant alternative. A variety of trigeneration technologies are available and their proper choice is influenced by the employed energy system conditions and preferences. In this paper, different types of trigeneration systems are classified according to the prime mover, size and energy sequence usage. A leveled selection procedure is subsequently listed in the consecutive sections. The first level contains the applied prime mover technologies which are considered to be the heart of any CCHP system. The second level comprises the heat recovery equipment (heating and cooling) of which suitable selection should be compatible with the used prime mover. The third level includes the thermal energy storage system and heat transfer fluid to be employed. For each section of the paper, a survey of conducted studies with CHP/CCHP implementation is presented. A comprehensive table of evaluation criteria for such systems based on energy, exergy, economy, and environment measures is performed, along with a survey of the methods used in their design, optimization, and decision-making. Moreover, a classification diagram of the main CHP/CCHP system components is summarized. A general selection approach of the appropriate CCHP system according to specific needs is finally suggested. In almost all reviewed works, CCHP systems are found to have positive technical and performance impacts. [ABSTRACT FROM AUTHOR]