Cell migration is an adaptive process that 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 bi-directional relationship of cell-tissue interactions (mechanoreciprocity) allows cells to change position and contributes to single-cell and collective movement, structural and molecular tissue organization, and cell fate decisions.