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We present a survey of recent developments in the field of sequential competitive location problems, including the closely related class of voting location problems, i.e. problems of locating resources as the result of a collective election. Our focus is on models where possible locations are not a priori restricted to a finite set of points. Furthermore, we restrict our attention to problems defined on networks. Since a line, i.e. an interval of one-dimensional real space, may be interpreted as a special type of network and because models defined on lines might contain ideas worth adopting in more general network models, we include these models as well, yet without describing them in detail for the sake of brevity.