Phenolic compounds are important constituents of plant-based foods, as their presence is related to protective effects on health. To exert their biological activity, phenolic compounds must be released from the matrix during digestion in an absorbable form (bioaccessible) and finally absorbed and transferred to the bloodstream (bioavailable). Chemical structure and matrix interactions are some food-related factors that hamper phenolic compounds bioaccessibility and bioavailability, and that can be counteracted by food processing. It has been shown that food processing can induce chemical or physical modifications in food that enhance phenolic compounds bioaccessibility and bioavailability. These changes include: (i) chemical modifications into more bioaccessible and bioavailable forms; (ii) cleavage of covalent or hydrogen bonds or hydrophobic forces that attach phenolic compounds to matrix macromolecules; (iii) damaging microstructural barriers such as cell walls that impede the release from the matrix; and (iv) create microstructures that protect phenolic compounds until they are absorbed. Indeed, food processing can produce degradation of phenolic compounds, however, it is possible to counteract it by modulating the operating conditions in favor of increased bioaccessibility and bioavailability. This review compiles the current knowledge on the effects of processing on phenolic compounds bioaccessibility or bioavailability, while suggesting new guidelines in the search of optimal processing conditions as a step forward towards the design of healthier foods.