Exchange bias and magnetic proximity effects are two novel phenomena that are in the limelight because of their fundamental and technological importance. Since both phenomena are interfacial in origin, we review these together. In the first part of this review, we have discussed the basics of these two phenomena. Subsequently, we have described numerous experimental examples involving a variety of composite magnetic materials and heterostructures. The recent theoretical models of these two interface phenomena have also been described. Finally, we have shed light on an obvious question: can one expect both these phenomena to occur together in any magnetically coupled system? We conclude that one can enhance the operating temperature of an exchange biased device by exploiting the magnetic proximity effect.