Simplicial volume was first introduced by Gromov to study the minimal volume of manifolds. Since then it has emerged as an active research field with a wide range of applications. In dimensions two and three, the set of simplicial volumes of orientable closed connected (occ) manifolds may be fully described using geometrization. Much less is known in higher dimensions. In joint work with Clara Löh (University of Regensburg), we show that the set of simplicial volumes in dimensions four and higher is dense in the non-negative reals. I will also motivate a conjecture on the precise set of simplicial volumes in dimension 4.