Power training (PT) improves muscle power in older adults; however, intensity recommendations are less clear. A narrative approach was used to compare high- versus low-intensity PT on muscle power (and function) in healthy, older adults. Searches were performed using Medline, Embase, CINAHL, SPORTDiscus, AgeLine, and Scopus. Interventions in which older subjects (60+ years) were instructed to perform the concentric phase “as fast as possible” were included. After searches were performed, a third category of PT (moderate intensity) was included. Evidence from 27 studies (32 PT groups) showed changes in muscle power that averaged 26.8%, 33.4%, and 21.5% for high-, moderate-, and low-intensity PT, respectively, with greater changes with longer training duration and in mildly mobility-limited older adults. Function improved similarly across categories. In conclusion, both low- and high-intensity PT led to clinically significant changes in power and are viable options for improving power and function in older adults.