This article emphasises that effectively teaching the application of geometrical tolerances poses a significant challenge for university lecturers and vocational training staff. The concise review of modern tools designed to promote the principles and rules of geometrical tolerances, thereby facilitating their successful implementation, is presented. A new series of recently developed animations is presented, aiming to show the roots of the Maximum Material Requirement (MMR) concept, which enables functional tolerancing that ensures assemblability. It is demonstrated that MMR is the specification tool that introduces an interdependency between dimensions and geometry. This allows mating parts with exceeded geometrical tolerances for their derived features, when the actual sizes of the features that have to be mated do not reach their maximum material sizes. Developed dynamic animations significantly improved the effectiveness of geometrical tolerancing lectures at the university and vocational education in industry. The establishment and movement of the tolerance zones and datum features, as well as the visualisations of the actual toleranced features and datums enable the clear and effective communication of complex geometrical tolerancing rules in a form readily understood by students.