Flame extinction represents one of the classical phenomena in combustion science. It is important to a variety of combustion systems in transportation and power generation applications. Flame extinguishment studies are also motivated from the consideration of fire safety and Suppression. Such studies have generally considered non-premixed and premixed flames, although fires can often originate in a partially premixed mode, i.e., fuel and oxidizer are partially premixed as they are transported to the reaction zone. Several recent investigations have considered this scenario and focused on the extinction of partially premixed flames (PPFs). Such flames have been described as hybrid flames possessing characteristics of both premixed and non-premixed flames. This paper provides a review of studies dealing with the extinction of PPFs, which represent a broad family of flames, including double, triple (tribrachial), and edge flames. Theoretical, numerical and experimental studies dealing with the extinction of such flames in coflow and counterflow configurations are discussed. Since these flames contain both premixed and non-premixed burning zones, a brief review of the dilution-induced extinction of premixed and non-premixed flames is also provided. For the coflow configuration, processes associated with flame liftoff and blowout are described. Since lifted non-premixed jet flames often contain a partially premixed or an edge-flame structure prior to blowout, the review also considers such flames. While the perspective of this review is broad focusing on the fundamental aspects of flame extinction and blowout, results mostly consider flame extinction caused by the addition of a flame suppressant, with relevance to fire suppression on earth and in space environment. With respect to the latter, the effect of gravity on the extinction of PPFs is discussed. Future research needs are identified. (C) 2009 Elsevier Ltd. All rights reserved.