The contribution, starting from an epistemological reflection that shows the connection between the categories of quality and quantity, passing through the construct of 'measurement', illustrates the evolution of quality assurance processes over the last fifty years, up to the current models of the so-called Total Quality Management. The application of these models to formal education and training contexts, with particular attention to the fields of Higher Education, poses numerous challenges and tasks that still need to be fully embraced both at the micro level of designing third-level courses of Higher Education (research doctorates) and at the macro level of overall policies, which, if they are to be considered of quality, should be supported by the effective exercise of autonomy.