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The cellular mechanical microenvironment can regulate many cellular physiological functions. In particular, cells can migrate directionally under external cue gradients from their mechanical microenvironment. These directed migrations play critical roles in wound healing, cancer cell metastasis and tissue morphology development. So far, directional cell migration mostly includes: the directional migration under chemical gradients (chemotaxis), the directional migration under adhesion gradients (haptotaxis), and the directional migration under mechanical gradients (durotaxis). Although the basic mechanisms of chemotaxis and haptotaxis are well characterized, the mechanism of durotaxis remains unclear. In this review, the experimental and theoretical advances in the study of cell durotaxis were described, the connections and differences among different studies were analyzed, the potential mechanical mechanism of cell durotaxis were discussed, and the remaining problems and possible future research directions were put forward. [ABSTRACT FROM AUTHOR]