# What are the current contenders/most promising approaches to High Tc Superconductivity?

I want to know what kinds of things theorists are currently looking at. Specifically, I want to know more about the promise that field-theoretic methods are showing. I am studying superconductivity at an advanced undergraduate/beginning graduate level. Links to review papers/papers appreciated. Thanks.

First note that High $T_C$ superconductivity may not have a general mechanism that works for all material, in opposition to the case of regular superconductivity and BCS theory. I mention this because there is an historical interplay between superconductivity and magnetism in the matter, as in Meissner effect.
Currently there are (roughly) two families of high $T_C$ superconductors, the cuprate family and the iron pnictides, which are material with different magnetic properties. Therefore the most promising approach might depend on the material in question.