Tropical Convex Hull Computations
  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. 
Michael Joswig