It is well known that the mechanical environment affects biological tissues. The importance of theories and models that aim at explaining the role of the mechanical stimuli in process such as differentiation and adaptation of tissues is highlighted because if those theories can explain the tissue’s response to mechanical loading and to its environment, it becomes possible to predict the consequences of mechanical stimuli on growth, adaptation and aging of tissues. This review aims to present an overview of the various theories and models on tissue differentiation and adaptation, and their mathematical implementation. Although current models are numerically well defined and are able to resemble the tissue differentiation and adaptation processes, they are limited by (1) the fact that some of their input parameters are likely to be site-and species-dependent, and (2) their verification is done by data that may make the model results redundant. However, some theories do have predictive power despite the limitations of generalization. It seems to be a matter of time until new experiments and models appear with predictive power and where rigorous verification can be performed.