Geometry has been taught for millennia and we have rather detailed references of the geometry taught in Scribal Schools in Babylon, 4000 years ago. Today, with the computer revolution and Artificial Intelligence available, nobody seems to be proposing we stop teaching Geometry. But which Geometry should we teach, why and how? What are the driving forces that influence each curriculum? How do the new computing tools open new pathways for Geometry teaching? We will mention in some detail the controversies around the official Syllabus in Portugal in the last decades to try to identify which are the prevalent ideas in the curriculum and which are the different cultures involved in the decision process, from a purely abstract approach to a more applied approach, that answer to different societal and cultural views and mix the proposals of mathematicians, mathematics educators and teachers in the classroom. We observe that amid societal changes and advances in knowledge, Geometry is always focused on Problem Solving, the use and exploration of diagrams to conjecture and achieve some kind of proof. We need to take intelligent paths to make the most of technology and not be a slave to it.