  We provide a review of recent advancements in nonlocal continuous models for
migration, mainly from the perspective of its involvement in embryonal
development and cancer invasion. Particular emphasis is placed on spatial
nonlocality occurring in advection terms, used to characterise a cell's
motility bias according to its interactions with other cellular and acellular
components in its vicinity (e.g., cell-cell and cell-tissue adhesions, nonlocal
chemotaxis), but we also shortly address spatially nonlocal source terms.
Following a brief introduction and motivation, we give a systematic
classification of available PDE models with respect to the type of featured
nonlocalities and review some of the mathematical challenges arising from such
models, with a focus on analytical aspects. Keywords: cell-cell and cell-tissue
adhesion; nonlocal and local chemotaxis; haptotaxis; classes of nonlocal
models; integro-differential equations; mathematical challenges.
