  We study generalisations to totally real fields of methods originating with
Wiles and Taylor-Wiles. In view of the results of Skinner-Wiles on elliptic
curves with ordinary reduction, we focus here on the case of supersingular
reduction. Combining these, we then obtain some partial results on the
modularity problem for semistable elliptic curves, and end by giving some
applications of our results, for example proving the modularity of all
semistable elliptic curves over $\mathbb{Q}(\sqrt{2})$.
