Modularity of residually reducible Galois representations

I will discuss joint work with Kris Klosin (CUNY) on the modularity of residually reducible Galois representations. When there are 2 or 3 residual pieces we have developed a general method to prove "R=T theorems". On the Galois side it relies on a careful study of the reducibility ideal of the universal deformation ring, the ideal corresponding to analogues of the Eisenstein ideal of the Hecke algebra.