Recent progress by a number of different groups and authors is reviewed on the stability properties of direct-spring pressure relief valves connected to pressure vessels with or without piping systems. Various different notions of stability and mechanisms for instability are revealed both in the case of gas and liquid service. It is stressed that it is not the valve itself that is stable or unstable, rather the harmful vibrations arise through interactions between the valve and its surroundings the inlet piping, the reservoir, and any outlet piping. A distinction is drawn between underlying instability mechanisms and flow these may be triggered during transient operations. The purpose of the work is to provide a coherent simplified account that will be of practical use for proposing new operational guidelines and mitigation strategies. Among these various mechanisms, oscillatory instability due to the interaction with a quarter wave acoustic mode in the inlet piping is argued to be the most important to mitigate. (C) 2017 Published by Elsevier Ltd.