Nanozymes are nanomaterials that exhibit enzyme-like catalytic activity, which have drawn increasing attention on account of their unique superiorities including very high robustness, low cost, and ease of modification. Metal–organic frameworks (MOFs) and covalent–organic frameworks (COFs) have emerged as promising candidates for nanozymes due to their abundant catalytic activity centers, inherent porosity, and tunable chemical functionalities. In this review, we first compare the enzyme-mimicking activity centers and catalytic mechanisms between MOF and COF nanozymes, and then summarize the recent research on designing and modifying MOF and COF nanozymes with inherent catalytic activity. Moreover, typical examples of sensing applications based on these nanozymes are presented, as well as the translation of enzyme catalytic activity into a visible signal response. At last, a discussion of current challenges is presented, followed by some future prospects to provide guidance for designing nanozyme sensors based on MOFs and COFs for practical applications.