Let W ∈ C[x1, ..., xn] be a polynomial. A pair of matrices f, g ∈ Mat(N, C[x1, ..., xn]) satisfying fg = gf = WidN is called a matrix factorization of W. I will review how matrix factorizations provide a model for D-brane categories. I will then discuss how matrix factorizations can be graded and equipped with a natural stability conditions. Finally, I will explain a prediction concerning the Floer cohomology of the real quintic.