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.