The classical Courant's nodal domain theorem states that the n-th eigenfunction of the Laplacian on a compact manifold has at most n nodal domains. The same holds for Steklov eigenfunctions on a compact manifold with boundary. The classical argument of the proof, however, does not apply to Dirichlet-to-Neumann eigenfunctions, which are the traces of Steklov eigenfunctions on the boundary. We disprove the conjectured validity of Courant's theorem for D-t-N eigenfunctions. Namely, given a smooth manifold M, and integers K,N, we built a Riemannian metric on M for which the n-th D-t-N eigenfunction has at least K nodal domains for all n=1,...,N. Based on a joint work with Angela Pistoia (Sapienza Università di Roma) and Alberto Enciso (ICMAT Madrid).