On an oriented surface $M$, the dynamics of a charged particle in a magnetic field is governed by a pair (g,$\lambda$) that consists of a Riemannian metric g together with a smooth function $\lambda$ modelling the magnetic field. If every unit speed particle moves on a closed orbit (and the minimal period depends continuously on the orbit), we call (g,$\lambda$) a Zoll magnetic system. We show that there is a plethora of such systems on every closed oriented surface, essentially one for every closed 1-form on $M$. In negative Euler characteristic these are the first examples beyond the trivial case (constant curvature and large constant magnetic field). The construction of Zoll magnetic systems is based on so-called transport twistor spaces and holomorphic blow-down maps into ruled surfaces. Based on joint work with Gabriel P. Paternain.