In this talk, I will describe how results from optimal control theory can be used to analyze equilibrium configurations of slender elastic structures. We will first review the Pontryagin maximum principle, which gives necessary conditions for a trajectory to be a local solution of an optimal control problem. We will then use this result to derive equilibrium conditions for flexible helical springs (e.g., a Slinky in its famous arch shape) and for slender inextensible surfaces (e.g., a strip of paper deformed into a Möbius band). Finally, we will use recent results for linear quadratic optimal control problems to make a conjecture on the stability of anisotropic elastic rods.