We will look at the eigenvalue of the magnetic Laplacian in a bounded domain in the plane, with uniform magnetic field and Neumann boundary conditions. This problem has been studied for a long time by physicists for its relevance to superconductivity, but many mathematical questions remain open. While previous work has mainly been concerned with asymptotic expansions for a large magnetic field, there has been a recent focus on explicit eigenvalue bounds.I will give an overview of joint work with Bruno Colbois, Luigi Provenzano and Alessandro Savo, in which we obtained upper and lower bounds for the eigenvalues, depending only on the value of the magnetic field and a few geometric parameters of the domain. In particular, I will describe a step toward the proof of a reverse Faber-Krahn inequality conjectured by Søren Fournais and Bernard Helffer. I will also present the results of a joint work with Bernard Helffer, which connects, in the case of the disk, the intensity of the magnetic field with the angular momentum of the first eigenfunction.