Cell migration is an adaptive process which depends on and responds to physical and molecular triggers. Moving cells sense and respond to tissue mechanics and induce transient or permanent tissue modifications, including extracellular matrix stiffening, compression and deformation, protein unfolding, proteolytic remodelling and jamming transitions. Here we discuss how the mechanoreciprocity of cell-tissue interactions allows cells to change position, and to define single-cell and collective movement, structural and molecular tissue organization, and cell fate decisions.