Modularity lifting theorems were introduced by Taylor and Wiles and formed a key part of the proof of Fermat's Last Theorem. Their method has been generalized successfully by a number of authors but always with the restriction that the Galois representations and automorphic representations in question have regular weight. I will describe a method to overcome this restriction in certain cases. I will focus mainly on the case of weight 1 elliptic modular forms. This is joint work with Frank Calegari.