Categorification is a recently discovered and a fast growing area of mathematics which includes Khovanov link homology and knot Floer homology theories. I will talk about relations between Khovanov link homology and chromatic graph cohomology. In the second part of the talk, I will introduce a calculus of planar diagrams that leads to categorification of the one-variable polynomial ring. This includes categorification of various orthogonal one variable polynomials, such as the Chebyshev polynomials of the second kind and Hermite polynomials.