Introduction
1 Semistable elliptic curves over Q are modular.
2 Why the semistability assumption?
3 All elliptic curves over Q are modular.
4 Kisin’s modularity lifting theorems.
5 Generalisations to totally real fields.
6 Potential modularity pre-Kisin and the p – λ trick.
7 Potential Modularity after Kisin.
8 Some final remarks.