Smooth interpolation of arbitrary curves and surfaces is a major problem in computer graphics. There are very successful variational formulations of similar problems in smooth interpolation of arbitrary functions; these have given rise to the (linear) theory of splines. However, there appears to be as yet no equivalent useful formulation of the general problem, so present computer graphics algorithms for cunres and surfaces use somewhat ad hoc extensions of the linear results based on parametric representations of splines and surface patches. The paper briefly describes the present state of affairs in the hope that variational geometers will pick up on some of these unsolved problems and develop a coherent theory of smooth interpolation of arbitrary geometrical objects. If such a theory can be developed, it may possibly revolutionize computer graphics.