The dental pulp is the inner part of the tooth responsible for properly functioning during its lifespan. Apart from the very big biological heterogeneity of dental cells, tooth microenvironments differ a lot in the context of mechanical properties—ranging from 5.5 kPa for dental pulp to around 100 GPa for dentin and enamel. This physical heterogeneity and complexity plays a key role in tooth physiology and in turn, is a great target for a variety of therapeutic approaches. First of all, physical mechanisms are crucial for the pain propagation process from the tooth surface to the nerves inside the dental pulp. On the other hand, the modulation of the physical environment affects the functioning of dental pulp cells and thus is important for regenerative medicine. In the present review, we describe the physiological significance of biomechanical processes in the physiology and pathology of dental pulp. Moreover, we couple those phenomena with recent advances in the fields of bioengineering and pharmacology aiming to control the functioning of dental pulp cells, reduce pain, and enhance the differentiation of dental cells into desired lineages. The reviewed literature shows great progress in the topic of bioengineering of dental pulp—although mainly in vitro. Apart from a few positions, it leaves a gap for necessary filling with studies providing the mechanisms of the mechanical control of dental pulp functioning in vivo.