Mineral ontogeny is the study of the growth and development of mineral deposits in general and, in the present context, speleothems in particular. Previous researchers, mainly in Russia, have developed a nomenclatural hierarchy based on the forms and habits of individual crystals and the assembly of individual crystals into both monomineralic and polymineralic aggegates (i.e. speleothems). Although investigations of the growth processes of speleothems are sparse, there is a large literature on growth processes of speleothem minerals and related crystals in the geochemical and materials science literature. The purpose of the present paper is to sort through the various concepts of crystal growth and attempt to relate these to observations on speleothems and to the Russian conceptual framework of mineral ontogeny. For calcite, the most common mineral in speleothems, the activation energy for two dimensional nucleation (required for the growth of large single crystals) is almost the same as the activation energy for three- dimensional nucleation (which would result in the growth of many small crystals). Calcite growth is highly sensitive to minor impurities that may poison growth in certain crystallographic directions or may poison growth altogether. Extensive recent research using the atomic force microscope (AFM) provides many details of calcite growth including the transition from growth on screw dislocations to growth by two-dimensional nucleation. The deposition of aragonite speleothems requires metastable supersaturation curve and is usually ascribed to the impurities Mg2+ and Sr2+. AFM studies reveal that Mg2+ poisons calcite growth by blocking deposition sites on dislocations, thus allowing supersaturation to build up past the aragonite solubility curve. Sr2+ precipitates as a Sr-rich nucleus with the aragonite structure which acts as a template for aragonite growth. The different morphology of gypsum speleothems can be explained by the different growth habit of gypsum. Examples of twinned growth, dendrite growth, and spherulitic growth are common in the crystal growth literature and can be used to interpret the corresponding cave forms. Interpretation of monomineralic aggregate growth follows from individual crystal mechanisms. Interpretation of polymineralic aggregate growth requires knowing the evolving chemistry which in turn requires new methods for the sampling and analysis of microliter or nanoliter quantities of fluid.