This paper provides a review on recent works in the field of competitive facility location models based on the following seven components: 1) Variables, 2) Competition type, 3) Solution space, 4) Customer behavior, 5) Demand type, 6) Number of new facilities and 7) Relocation and redesign possibility. First, the components are introduced and then based on these components; different studies are compared with each other via a proposed taxonomy and finally a review on work of each paper is provided.