Nanoparticulate materials displaying enzyme-like properties, so-called nanozymes, are explored as substitutes for natural enzymes in several industrial, energy-related, and biomedical applications. Outstanding high stability, enhanced catalytic activities, low cost, and availability at industrial scale are some of the fascinating features of nanozymes. Furthermore, nanozymes can also be equipped with the unique attributes of nanomaterials such as magnetic or optical properties. Due to the impressive development of nanozymes during the last decade, their potential in the context of tissue engineering and regenerative medicine also started to be explored. To highlight the progress, in this review, we discuss the two most representative nanozymes, namely, cerium- and iron-oxide nanomaterials, since they are the most widely studied. Special focus is placed on their applications ranging from cardioprotection to therapeutic angiogenesis, bone tissue engineering, and wound healing. Finally, current challenges and future directions are discussed.