Plants are rich in bioactive compounds (BACs), mainly polyphenols, which are valuable choices to replace synthetic antioxidants in meat products. These natural antioxidants from plants, in the form of extracts and essential oils (EOs), have been obtained from different sources such as fruits (dragon fruit, guarana, pomegranate), vegetables, (cabbage, onion), herbs, and spices (epazote, ginger, rosemary, sage, thyme, turmeric, winter savory) by several extraction processes. However, in the context of current directives there is a notable incentive for “green” solvents to replace organic ones and conventional techniques, in order to avoid harm to the environment, operator, and consumer health. In addition, the recycling of co-products from the processing of these plant materials allow us to obtain valuable BACs from under-exploited materials, contributing to the revalorization of these wastes. The resulting extracts allow us to maintain the quality of meat products, exhibiting similar or better antioxidant properties compared to those shown by synthetic ones. Their incorporation in fresh meat products would maintain the oxidative stability, stabilizing colour parameters, decreasing the formation of metmyoglobin, lipid, and protein oxidation and the generation of lipid-derived volatile compounds, without affecting sensory attributes. In addition, these novel ingredients contribute to improve both technological and functional characteristics, thus diversifying the offer of so-called “wellness foods”. In this review, the application of plant extracts as natural antioxidants in several fresh meat products is presented, showing their efficacy as scavenging radicals and imparting additional health benefits.