Competitive facility location problems are concerned with thefollowing situation: a firm wants to locate a predefined num-ber of facilities to serve customers locate in some region wherethere already exist (or will be) other firms offering the sameservice. Both new and existing firms compete for optimizingtheir market share of profit. A discrete version of such problemsarises when it is assumed that there is a ( rather small ) finitenumber of candidate locations and the markets consist of pointdemands. We review modelling and optimization approaches forthis type of problems and we emphasize and develop the bi-levelprogramming methodology.