I will present some results on Schrödinger operators with a magnetic potential of Aharonov-Bohm type. This means that the magnetic potential has singularities at a finite number of points called poles. On a bounded planar domain, we define the corresponding magnetic Hamiltonians with Dirichlet boundary conditions, and study their eigenvalues as functions of the poles. The nodal sets of the eigenfunctions is connected to a spectral minimal partition problem. These eigenvalues are shown to be continuous. Using Kato-Rellich theory, they can even be shown to be analytic under some restrictive conditions.