2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171162This is a survey on tropical polytopes from the combinatorial point of view and with a focus on algorithms. Tropical convexity is interesting because it relates a number of combinatorial concepts including ordinary convexity, monomial ideals, subdivisions of products of simplices, matroid theory, finite metric spaces, and the tropical Grassmannians. The relationship between these topics is explained via one running example throughout the whole paper. The final section explains how the new version 2.9.4 of the software system polymake can be used to compute with tropical polytopes.18 pages, 3 figures; minor additions and corrections; to appear in Contemporary MathematicsCombinatoricsMetric Geometry05B35; 52B40; 14M15text