The recent discovery of magnetism in monolayers of two-dimensional van der Waals materials has opened new venues in materials science and condensed matter physics. Until recently, two-dimensional magnetism remained elusive: Spontaneous magnetic order is a routine instance in three-dimensional materials but it is not a priori guaranteed in the two-dimensional world. Since the 2016 discovery of antiferromagnetism in monolayer FePS3 by two groups and the subsequent demonstration of ferromagnetic order in monolayer CrI3 and bilayer Cr2Ge2Te6, the field changed dramatically. Within several years of scientific discoveries focused on 2D magnets, novel opportunities have opened up in the field of spintronics, namely spin pumping devices, spin transfer torque, and tunneling. In this review, we describe the state of the art of the nascent field of magnetic two-dimensional materials focusing on synthesis, engineering, and theory aspects. We also discuss challenges and some of the many different promising directions for future work, highlighting unique applications that may extend even to other realms, including sensing and data storage.