Although historically grown as independent energy technologies, fuel cell and cogeneration may adequately work to each other’s benefit. Some fuel cells deliver heat at sufficiently high temperatures, which can be certainly used as heat sources for cogeneration or trigeneration schemes. The paper presents an overview of the innumerable fuel cell system configurations for simultaneous production of (i) heat and power, (ii) cooling and electricity, and (iii) cooling, heat, and electricity. The survey includes combined power cycles (also called hybrid systems) where the fuel cell works together with other thermodynamic cycles to produce, with a high fuel-to-electricity efficiency, electricity alone. A large number of cogeneration arrangements are mentioned. Some are described in detail. A brief analysis of benefits and drawbacks of such systems was undertaken. The review was limited to articles published in archival periodicals, proceedings, and a few technical reports, theses, and books.