Fruits and fruit products are an essential part of the human diet. Their health benefits are directly related to their content of valuable bioactive compounds, such as polyphenols, anthocyanins, or vitamins. Heat treatments allow the production of stable and safe products; however, their sensory quality and chemical composition are subject to significant negative changes. The use of emerging non-thermal technologies, such as HPP (High Pressure Processing), has the potential to inactivate the microbial load while exerting minimal effects on the nutritional and organoleptic properties of food products. HPP is an adequate alternative to heat treatments and simultaneously achieves the purposes of preservation and maintenance of freshness characteristics and health benefits of the final products. However, compounds responsible for antioxidant activity can be significantly affected during treatment and storage of HPP-processed products. Therefore, this article reviews the effect of HPP treatment and subsequent storage on the antioxidant activity (oxygen radical absorbance capacity (ORAC) assay), 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical scavenging capacity assay, ferric reducing antioxidant power (FRAP) assay, 2,2′-azino-bis-(3-ethylbenzothiazoline-6-sulfonic acid) (ABTS) radical scavenging capacity assay or Trolox equivalent antioxidant capacity (TEAC) assay), and on the total phenolic, flavonoid, carotenoid, anthocyanin and vitamin contents of fruits and different processed fruit-based products.