After recalling the Jones polynomial of a knot, we will sketch the definition of two refinements: Khovanov homology and a Khovanov stable homotopy type. We will then discuss briefly how, following ideas of Lee, Ozsvath-Szabo, and Rasmussen, these can be used to obtain results about surfaces in 4-space bounded by a knot. This is joint work with Tyler Lawson and Sucharit Sarkar. There is related work by Hu-Kriz-Kriz.