There are many extension theorems in mathematics: Tietze Extension, Whitney's Extension, and Hahn-Banach just to name a few. I will show that it is a surprisingly easy task to extend uniformly continuous functions between two Hilbert spaces. I will focus mainly on the Lipschitz case and show how the extension question is tied directly to the geometry of the closed balls in the space. A short discussion about the geometries of non-Hilbert spaces that do and do not give the conditions will also be given.