Considering the current techniques in cell culture, the stimulation of cellular proliferation and the formation of bidimensional tissues such as skin are widely performed in academic and industrial research laboratories. However, the formation of cohesive, organized, and functional tissues by three-dimensional (3D) cell culture is complex. A suitable environment is required, which is achieved and maintained in a specific bioreactor, a device that reproduces the physiological environment (including biochemical and mechanical functions) specific to the tissue that is to be regenerated. Bioreactors can also be used to apply mechanical constraints during maturation of the regenerating tissue for studying and understanding the mechanical factors influencing tissue regeneration. In this work, the main types of bioreactors used for tissue engineering and regeneration, as well as their most common applications, were reviewed and compared. The importance of the mechanical properties applied to the scaffolds and the regenerating constructs has been often neglected. This review focused on the influence of mechanical stresses and strains during the culture period that leads to the final mechanical properties of the construct.