Many computer programs have been produced which are designed to teach geometry. To do this, the writers of these programs have had to examine the nature of geometrical activity in great detail. Setting up models of what an expert does when tackling a geometrical problem has demonstrated the considerably complex nature of the task. The need to describe geometrical proof with all its detail, shows the large number of implicit steps which proof requires and this, of course complicates the task for the learner. The difficulty of identifying the heuristics used by experts employing geometrical reasoning, allows us to appreciate the variety and the complexity of arguments used. Lastly, the absence of software which can compare with the global human view of a geometrical figure, makes the detection of relevant sub- figures difficult: this requires geometry programs to make long and often fruitless detours. Faced with these difficulties, researchers have rediscovered the vital importance of the figure in geometrical proof and they are now trying to understand the subtle synergy that exists between the geometrical figure and geometrical reasoning. Although, despite recent improvements, programs for teaching proof in geometry are still far from being equal to what an expert does, the work, that has gone into producing them has helped us to have a greater understanding of the enormous complexity of geometrical activity and its underlying character. Teaching geometry needs, therefore, to be fundamentally modified. (ZDM/Mathdi)