  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.
