Crawling of animal cells is a crucial part of morphogenesis and wound healing. The phenomenon ofcrawling was dissected by Abercrombie two decades ago into the simpler processes of: (i) protrusion, (ii) attachment, (iii) contraction, (iv) detachment, (v) forward translocation.

In the recent years, both experimental and theoretical advances produced the models of Polymerization Ratchet, Dynamic Actomyosin Contraction and Graded Radial Attachment attempting to explain these processes separately. The coordination of the locomotion, though still poorly understood, also is tried to be elucidated with the concept of Molecular Clutch. I will review the current state of the field and discuss the current models and results, both biological and mathematical.

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1998-1999 Mathematics in Biology