After homeomorphisms, the next simplest type of maps on manifolds are called cellular maps. When these maps are not homeomorphisms, techniques to measure the complexity of their images are needed. A key measure of complexity is that of codimension of certain subsets of the image. In finite dimensional manifolds, codimension is easily understood. We will give a few basic examples illustrating cellularity and codimension and if time permits, show what the analogous concepts are in the Hilbert Cube.