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In this article, we propose a state of the art concerning the nodal andspectral minimal partitions. First we focus on the nodal partitions and givesome examples of Courant sharp cases. Then we are interested in minimalspectral partitions. Using the link with the Courant sharp situation, we candetermine the minimal k-partitions for some particular domains. We also recallsome results about the topology of regular partitions and Aharonov-Bohmapproach. The last section deals with the asymptotic behavior of minimalk-partition.

Nodal and spectral minimal partitions -- The state of the art in 2015 --