Measuring the antioxidant activity/capacity levels of food extracts and biological fluids is useful for determining the nutritional value of foodstuffs and for the diagnosis, treatment, and follow-up of numerous oxidative stress-related diseases. Biologically, antioxidants play their health-beneficial roles via transferring a hydrogen (H) atom or an electron (e(-)) to reactive species, thereby deactivating them. Antioxidant activity assays imitate this action; that is, antioxidants are measured by their H atom transfer (HAT) ore transfer (ET) to probe molecules. Antioxidant activity/capacity can be monitored by a wide variety of assays with different mechanisms, including HAT, ET, and mixed-mode (ET/HAT) assays, generally without distinct boundaries between them. Understanding the principal mechanisms, advantages, and disadvantages of the measurement assays is important for proper selection of method for valid evaluation of antioxidant properties in desired applications. This work provides a general and up-to-date overview of HAT-based, mixed-mode (ET/HAT), and lipid peroxidation assays available for measuring antioxidant activity/capacity and the chemistry behind them, including a critical evaluation of their advantages and drawbacks.