On the work of Ritter and Weiss in Comparison with Kakde's Approach

Almost simultaneously Ritter and Weiss arXiv:1004.2578 on the one hand and Kakde arXiv:1008.0142 on the other hand gave a proof of the non-commutative Iwasawa main conjecture over totally real fields for the Tate motive under the assumption that a certain $\mu$-invariant vanishes as has been conjectured also by Iwasawa. In this notes we compare both approaches in a survey.