In this talk, I will present mechanobiochemical models for 2- and 3-D cell migration, from single to collective, based on geometric bulk-surface partial differential equations (G-BS-PDEs). The first model is a geometric surface PDE approach where the cell is described by its cell membrane which obeys a force balance equation for its evolution. This approach encodes naturally the biochemical processes and biomechanical properties of the cells and its interactions with deformable obstacles, and cell-to-cell interactions. I will also present a generalisation to include interior cell dynamics for cells migrating in confinement. The second model consists of an optimal control model based on geometric multigrid methods for a diffuse-interface formulation. This approach allows us to model the spatiotemporal dynamics of static experimental images of migrating cells. A by-product of this methodology is the automatic quantification of proliferation rates associated with cell division. A third and final approach is a viscoelastic model, where the displacements of the cell are driven by biomolecular species which obey a reaction-diffusion system. Numerical results will be presented to illustrate the novelty of these mechanobiochemical models for single and collective cell migration. Single and collective cell migration are essential for physiological, pathological and biomedical processes in development, repair, and disease; for example, in embryogenesis, wound healing, immune response, cancer metastasis, tumour invasion, and inflammation.