When locating a new facility, a company should take into account the reaction of possible competitors. In continuous location, this leads to challenging Global Optimization problems. The competition can also enhance price competition, or competing with quality to attract more customers. We observe that in location science this is typically dealt with from a bi-level way of thinking, where optimization of the competitive prices and quality is done on a second level and substituted into a first level decision. Moreover, the reaction of the competitor can be considered a second level decision in a so-called leader-follower (Stackelberg) setting leading potentially to tri-level analysis. One can also focus on Nash equilibria from the location perspective where one tries to find whether stable market situations in terms of competition, location or quality competition exist. This setting gives rise to many studies that focus on optimality conditions and algorithms that make use of these conditions in order to find the best location for the competing firm. We will sketch several interesting cases that lead to multiple studies on the subject.