  This 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.
