Add to ORKGConcurrency ie the domain in computer science which deals with parallel asynchronous computations has very strong links with alge braic topology this is what we are developing in this paper giving a survey of geometric models for concurrency We show that the prop erties we want to prove on concurrent systems are stable under some form of deformation which is almost homotopy In fact as the direc tion of time matters we have to allow deformation only as long as we do not reverse the direction of time This calls for a new homotopy theory directed or dihomotopy We develop some of the geometric intuition behind this theory and give some hints about the algebraic objects one can associate with it in particular homology groups Fo...