The main focus of this study is on competitive facility location problems which constitute a special family of facility location problems. In such a problem, a firm or franchise is concerned with installing new facilities to serve customers in a market where existing facilities with known locations and attractiveness levels compete for increasing their market share and profit. We can classify these problems into two groups: those with non-reactive competition and those with reactive competition. In this study, three different types of competitive facility location models are proposed in order to determine the locations and attractiveness levels of the new facilities to maximize the profit. The first one belongs to the former class, where the last two models fall into the latter one and therefore bring us to the area of the bilevel programming. Finally, a different facility location problem which takes the customer preferences into account is considered, where the facilities are not necessarily identical and customers visit different types of facilities according to some given probability distribution and the maximum distance which they are willing to travel.