Polyphenols, as well as volatile compounds responsible for aromatic features, play a critical role in the quality of vegetables and medicinal, and aromatic plants (MAPs). The research conducted in recent years has shown that these plants contain biologically active compounds, mainly polyphenols, that relate to the prevention of inflammatory processes, neurodegenerative diseases, cancers, and cardiovascular disorders as well as to antimicrobial, antioxidant, and antiparasitic properties. Throughout the years, many researchers have deeply studied polyphenols and volatile compounds in medicinal and aromatic plants, particularly those associated with consumer’s choices or with their beneficial properties. In this context, the purpose of this review is to provide an overview of the presence of volatile and nonvolatile compounds in some of the most economically relevant and consumed vegetables and medicinal and aromatic plants, with an emphasis on bioactive polyphenols, polyphenols as prebiotics, and, also, the most important factors that affect the contents and profiles of the volatile and nonvolatile compounds responsible for the aromatic features of vegetables and MAPs. Additionally, the new challenges for science in terms of improving polyphenol composition and intensifying volatile compounds responsible for the positive characteristics of vegetables and medicinal and aromatic plants are reported.