In recent times, there has been a significant increase in researchers’ interest in the functions of microRNAs and the role of these molecules in the pathogenesis of many multifactorial diseases. This is related to the diagnostic and prognostic potential of microRNA expression levels as well as the prospects of using it in personalized targeted therapy. This review of the literature analyzes existing scientific data on the involvement of microRNAs in the molecular and cellular mechanisms underlying the development of pathologies such as Alzheimer’s disease, cerebral ischemia and reperfusion injury, and dysfunction of the blood–brain barrier.