Some Algorithmic Problems in Polytope Theory

This is a survey on algorithmic questions about combinatorial and geometric properties of convex polytopes. We give a list of 35 problems; for each the current state of knowledege on its theoretical complexity status is reported. The problems are grouped into the sections Coordinate Descriptions'', Combinatorial Structure’‘, Isomorphism'', Optimization’‘, Realizability'', and Beyond Polytopes’'.