Combined generation units of heat and power, known as CHP units, are one of the most prominent applications of distributed generations in modern power systems. This concept refers to the simultaneous operation of two or more forms of energy from a simple primary source. Due to the numerous environmental, economic, and technical advantages, the use of this technology in modern power systems is highly emphasized. As a result, various issues of interest in the control, operation, and planning of power networks have experienced significant changes and faced important challenges. In this way, the unit commitment problem (UCP) as one of the fundamental studies in the operation of integrated power, and heat systems have experienced some major conceptual and methodological changes. This work, as a complementary review, details the CHP-based UCP (CHPbUCP) in terms of objective functions, constraints, simulation tools, and applied hardwares. Furthermore, some useful data on case studies are provided for researchers and operators. Finally, the work addresses some challenges and opens new perspectives for future research.