Through the years, mineralogical studies have produced a tremendous amount of data on the atomic arrangement and mineral properties. Quite often, structural analysis has led to elucidate the role played by minor components, giving interesting insights into the physico-chemical conditions of minerals and allowing the description of unpredictable structures that represented a body of knowledge critical for assessing their technological potentialities. Using such a rich database, containing many basic acquisitions, further steps became appropriate and possible, into the directions of more advanced knowledge frontiers. Some of these frontiers assume the name of modularity, complexity, aperiodicity, and matter organization at not conventional levels, and will be discussed in this review.