Spintronics is concerned with replacing charge current with current of spin, the electron's intrinsic angular momentum. In magnetic insulators, spin currents are carried by magnons, the quanta of spin-wave excitations on top of the magnetically ordered state. Magnon spin currents are especially promising for information technology due to their low intrinsic damping, non-reciprocal transport, micrometer wavelengths at microwave frequencies, and strong interactions that enable signal transduction. In this perspective, we give our view on the progress and challenges toward realizing magnon spintronics based on atomically thin van der Waals magnets, a recently discovered class of magnetic materials of which the tunability and versatility have attracted a great deal of ongoing research.