The Dirichlet type space D(mu) is the space of all analytic functions f on the open unit disc such that f’is square integrable with respect to the superharmonic weight U_mu dA. We first introduce the background for the D(mu) space. Then we talk about the corona theorem and the Wolff theorem for the D(mu) space, we will also talk about the multipliers for the harmonic Dirichlet-type space.