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This paper presents a review of the different models developed for the taxicab problem. The presented models are grouped in two categories, aggregated and equilibrium models. Each model is analyzed from different points of view, such as market organization, operational organization and regulation issues. Conclusions extracted by authors are presented, listed and compared, analyzing each affirmation in terms of market regulation and organization. Finally, a state of the practice is presented, analyzing the configuration of the taxi market regulations along the world, linking the conclusions obtained by the authors with the real market situations.