Phenolic compounds are bioactive phytochemicals showing a wide range of pharmacological activities, including anti-inflammatory, antioxidant, immunomodulatory, and anticancer effects. Moreover, they are associated with fewer side effects compared to most currently used antitumor drugs. Combinations of phenolic compounds with commonly used drugs have been largely studied as an approach aimed at enhancing the efficacy of anticancer drugs and reducing their deleterious systemic effects. In addition, some of these compounds are reported to reduce tumor cell drug resistance by modulating different signaling pathways. However, often, their application is limited due to their chemical instability, low water solubility, or scarce bioavailability. Nanoformulations, including polyphenols in combination or not with anticancer drugs, represent a suitable strategy to enhance their stability and bioavailability and, thus, improve their therapeutic activity. In recent years, the development of hyaluronic acid-based systems for specific drug delivery to cancer cells has represented a pursued therapeutic strategy. This is related to the fact that this natural polysaccharide binds to the CD44 receptor that is overexpressed in most solid cancers, thus allowing its efficient internalization in tumor cells. Moreover, it is characterized by high biodegradability, biocompatibility, and low toxicity. Here, we will focus on and critically analyze the results obtained in recent studies regarding the use of hyaluronic acid for the targeted delivery of bioactive phenolic compounds to cancer cells of different origins, alone or in combination with drugs.