The Hardy inequality which is now 96 years old has developed into a useful tool in mathematical physics, partial differential equations, interpolation theory etc. The Rellich inequality which is a youthful 63 is less well known and has had less applications. In this talk we summarize some background information on these inequalities, discuss their relationships and describe conditions which allow one to deduce the Rellich inequality from the Hardy inequality. In particular we explain how both inequalities are usefully rephrased as part of the general theory of local Dirichlet forms.