In this article, we propose a state of the art concerning the nodal and
spectral minimal partitions. First we focus on the nodal partitions and give
some examples of Courant sharp cases. Then we are interested in minimal
spectral partitions. Using the link with the Courant sharp situation, we can
determine the minimal k-partitions for some particular domains. We also recall
some results about the topology of regular partitions and Aharonov-Bohm
approach. The last section deals with the asymptotic behavior of minimal
k-partition
