Abstract: Bicycle is modeled as a directed segment of a fixed length that can move so that the velocity of the rear end is always aligned with the segment. A bicycle path is a motion of the segment, subject to this nonholonomic constraint, and the length of the path, by definition, is the length of the front track. This defines a problem of sub-Riemannian geometry, and one wants to describe the respective geodesics. I shall discus three variations on this theme: the planar bicycle motion, the bicycle motion in multidimensional Euclidean space, and the planar motion of a 2-linkage (a tricycle?) Somewhat unexpectedly, these problems are closely related with the filament equation, a completely integrable system of soliton type, whose soliton curves appear as the sub-Riemannian geodesics