Combined Heat and Power (CHP) is the sequential or simultaneous generation of multiple forms of useful energy, usually electrical and thermal, in a single and integrated system. Implementing CHP systems in the current energy sector may solve energy shortages, climate change and energy conservation issues. This review paper is divided into six sections: the first part defines and classifies the types of fuel cell used in CHP systems; the second part discusses the current status of fuel cell CHP (FC-CHP) around the world and highlights the benefits and drawbacks of CHP systems; the third part focuses on techniques for modelling CHP systems. The fourth section gives a thorough comparison and discussion of the two main fuel cell technologies used in FC-CHP (PEMFC and SOFC), characterising their technical performance and recent developments from the major manufacturers. The fifth section describes all the main components of FC-CHP systems and explains the issues connected with their practical application. The last part summarises the above, and reflects on micro FC-CHP system technology and its future prospects.