The notion of unrolling of a spherical curve is proved to coincide with its
development into the tangent plane. The development of a curve in an arbit
rary surface in the Euclidean 3-space is then studied from the point of vie
w of unrolling. The inverse operation, called the rolling of a curve onto a
surface, is also analysed and the relationship of such notions with the fu
nctional defined by the square of curvature is stated. An application to th
e construction of nonlinear splines on Riemannian surfaces is suggested.