We assess performance and limitations of polygenic risk scores (PRSs) for multiple blood pressure (BP) phenotypes in diverse population groups. We compare “clumping-and-thresholding” (PRSice2) and LD-based (LDPred2) methods to construct PRSs from each of multiple GWAS, as well as multi-PRS approaches that sum PRSs with and without weights, including PRS-CSx. We use datasets from the MGB Biobank, TOPMed study, UK biobank, and from All of Us to train, assess, and validate PRSs in groups defined by self-reported race/ethnic background (Asian, Black, Hispanic/Latino, and White). For both SBP and DBP, the PRS-CSx based PRS, constructed as a weighted sum of PRSs developed from multiple independent GWAS, perform best across all race/ethnic backgrounds. Stratified analysis in All of Us shows that PRSs are better predictive of BP in females compared to males, individuals without obesity, and middle-aged (40-60 years) compared to older and younger individuals.