The leaching of minerals is one of the main unit operations in the metal dissolution process, and in turn it is a process that generates fewer environmental liabilities compared to pyrometallurgical processes. As an alternative to conventional leaching methods, the use of microorganisms in mineral treatment processes has become widespread in recent decades, due to advantages such as the non production of emissions or pollution, energy savings, low process costs, products compatible with the environment, and increases in the benefit of low-grade mining deposits. The purpose of this work is to introduce the theoretical foundations associated with modeling the process of bioleaching, mainly the modeling of mineral recovery rates. The different models are collected from models based on conventional leaching dynamics modeling, based on the shrinking core model, where the oxidation process is controlled by diffusion, chemically, or by film diffusion until bioleaching models based on statistical analysis are presented, such as the surface response methodology or the application of machine learning algorithms. Although bioleaching modeling (independent of modeling techniques) of industrial (or large-scale mined) minerals is a fairly developed area, bioleaching modeling applied to rare earth elements is a field with great growth potential in the coming years, as in general bioleaching has the potential to be a more sustainable and environmentally friendly mining method than traditional mining methods.