Isogenies of elliptic curves over finite fields have been well-studied, in part because there are several cryptographic applications. Using Velu’s formula, isogenies can be constructed explicitly given their kernel. Velu’s formula applies to elliptic curves given by a Weierstrass equation. In this paper we show how to similarly construct isogenies on Edwards curves and Huff curves. Edwards and Huff curves are new normal forms for elliptic curves, different than the traditional Weierstrass form.