The discovery of magnetism by the ancient Greeks was enabled by the natural occurrence of lodestone - a magnetized version of the mineral magnetite. Nowadays, natural minerals continue to inspire the search for novel magnetic materials with quantum-critical behaviour or exotic ground states such as spin liquids. The recent surge of interest in magnetic frustration and quantum magnetism was largely encouraged by crystalline structures of natural minerals realizing pyrochlore, kagome, or triangular arrangements of magnetic ions. As a result, names like azurite, jarosite, volborthite, and others, which were barely known beyond the mineralogical community a few decades ago, found their way into cutting-edge research in solid-state physics. In some cases, the structures of natural minerals are too complex to be synthesized artificially in a chemistry lab, especially in single-crystalline form, and there is a growing number of examples demonstrating the potential of natural specimens for experimental investigations in the field of quantum magnetism. On many other occasions, minerals may guide chemists in the synthesis of novel compounds with unusual magnetic properties. The present review attempts to embrace this quickly emerging interdisciplinary field that bridges mineralogy with low-temperature condensed-matter physics and quantum chemistry.