In the present paper we give a historical account -ranging from classical to
modern results- of the problem of rolling two Riemannian manifolds one on the
other, with the restrictions that they cannot instantaneously slip or spin one
with respect to the other. On the way we show how this problem has profited
from the development of intrinsic Riemannian geometry, from geometric control
theory and sub-Riemannian geometry. We also mention how other areas -such as
robotics and interpolation theory- have employed the rolling model.Comment: 20 page
