In this article, we analyzed the dynamics of the population aging process in Europe. The study was conducted on the basis of statistical data on the number of people aged 65 and above per 1000 of the population in 32 European countries in the years 1991–2018. The analyses also took into account the structure of the population by gender in five age groups: 65–69, 70–74, 75–79, 80–84, and 85 and above. An extensive analysis of the rate of changes in the magnitude of the phenomenon was carried out, which gave an answer to the question about how quickly Europe is aging. We applied the spatial dynamic shift–share method. The spatial variant of the method allowed, among others, indicating countries where the pace of population aging in a specific age group was faster/slower than in locations neighboring the examined country. Specific regions characterized by the fastest population aging were also indicated, and shares of structural and sectoral factors of the changes were estimated. Furthermore, based on the values of local competitiveness indicators, regions were identified where the aging of the population decelerated or accelerated the phenomenon in neighboring countries in the study period.