Infinite dimensional manifolds arise naturally even from considerations of finite dimensional spaces. But in general, infinite dimensional topological vector spaces lose many of the nice properties from the finite case that we casually take for granted in differential geometry. In this talk, we consider the nicer cases of Banach and Hilbert spaces and manifolds modeled on these. The basic building blocks of differential geometry (like charts, smooth structures, and tangent vectors) can be easily defined, and we will observe some differences and similarities between the finite theories of submanifolds and vector bundles and their respective general Banach/Hilbert counterparts.