Two-dimensional (2D) materials provide a platform for developing novel spintronic devices and circuits for low-power electronics. In particular, inducing magnetism and injecting spins in graphene have promised the emerging field of graphene spintronics. This review focuses on the magnetic proximity effect at the interface of 2D materials and magnetic oxide insulators. We highlight the unique spin-related phenomena arising from magnetic exchange interaction and spin-orbital coupling in 2D materials coupled with magnetic oxides. We also describe the fabrication of multifunctional hybrid devices based on spin transport. We conclude with a perspective of the field and highlight challenges for the design and fabrication of 2D spintronic devices and their potential applications in information storage and logic devices.