Cognitive impairment, also known as cognitive decline, can occur gradually or suddenly and can be temporary or more permanent. It represents an increasingly important public health problem and can depend on normal aging or be linked to different neurodegenerative disorders, including Alzheimer’s disease (AD). It is now well-established that lifestyle factors including dietary patterns play an important role in healthy aging as well as in the prevention of cognitive decline in later life. Among the natural compounds, dietary polyphenols including phenolic acids have been recently the focus of major attention, with their supplementation being associated with better cognitive status and prevention of cognitive decline. Despite their therapeutic potential, human studies investigating the relation between phenolic acids intake and cognitive outcomes are rather scarce. In this review, we provide preclinical evidence that different dietary polyphenols such as rosmarinic acid, ellagic acid, and cinnamic aldehyde can exert neuroprotective and pro-cognitive activities through different molecular mechanisms including the modulation of pro-oxidant and antioxidant machinery as well as inflammatory status. Future and more numerous in vivo studies are needed to strengthen the promising results obtained at the preclinical level. Despite the excellent pharmacokinetic properties of phenolic acids, which are able to be accumulated in the brain at pharmacologically relevant levels, future studies should also identify which among the different metabolites produced as a consequence of phenolic acids’ consumption may be responsible for the potential neuroprotective effects of this subgroup of polyphenols.