Iwasawa theory
More recently, also modeled upon Ribet's method, Chris Skinner and Eric Urban have announced a proof of a main conjecture for GL(2). An easier proof of the Mazur-Wiles theorem can be found by using Euler systems as developed by Kolyvagin (see Washington's book). Other generalizations of the main conjecture proved using the Euler system method have been found by Karl Rubin, amongst others.