By controlling several antioxidant and detoxifying genes at the transcriptional level, including NAD(P)H quinone oxidoreductase 1 (NQO1), multidrug resistance-associated proteins (MRPs), UDP-glucuronosyltransferase (UGT), glutamate-cysteine ligase catalytic (GCLC) and modifier (GCLM) subunits, glutathione S-transferase (GST), sulfiredoxin1 (SRXN1), and heme-oxygenase-1 (HMOX1), the KEAP1/NRF2 pathway plays a crucial role in the oxidative stress response. Accordingly, the discovery of modulators of this pathway, activating cellular signaling through NRF2, and targeting the antioxidant response element (ARE) genes is pivotal for the development of effective antioxidant agents. In this context, natural products could represent promising drug candidates for supplementation to provide antioxidant capacity to human cells. In recent decades, by coupling in silico and experimental methods, several natural products have been characterized to exert antioxidant effects by targeting the KEAP1/NRF2 pathway. In this review article, we analyze several natural products that were investigated experimentally and in silico for their ability to modulate KEAP1/NRF2 by non-covalent and covalent mechanisms. These latter represent the two main sections of this article. For each class of inhibitors, we reviewed their antioxidant effects and potential therapeutic applications, and where possible, we analyzed the structure-activity relationship (SAR). Moreover, the main computational techniques used for the most promising identified compounds are detailed in this survey, providing an updated view on the development of natural products as antioxidant agents.