  In this survey, we review the properties of minimal spectral $k$-partitions
in the two-dimensional case and revisit their connections with Pleijel's
Theorem. We focus on the large $k$ problem (and the hexagonal conjecture) in
connection with two recent preprints by J. Bourgain and S. Steinerberger on the
Pleijel Theorem. This leads us also to discuss some conjecture by I.
Polterovich, in relation with square tilings. We also establish a Pleijel
Theorem for Aharonov-Bohm Hamiltonians and deduce from it, via the magnetic
characterization of the minimal partitions, some lower bound for the number of
critical points of a minimal partition.
