The paper gives a survey on the development of dual (or outer) billiards since the introduction of the notion by \textit{J. Moser} [Is the solar system stable? Math. Intell. 1, 65--71 (1978)]. The following topics are addressed: the area-preserving property, how to recover a billiard from an invariant curve, duality between inner and outer billiards, behaviour at infinity and boundedness results for billiards given by rational and by quasi-rational polygons, dual billiards in the hyperbolic plane, and, very briefly, multidimensional dual billiards.