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Abstract The maximum intrinsic rate of population increase (r_max) represents a population's maximum capacity to replace itself and is central to fisheries management and conservation. Species with lowerr_maxtypically have slower life histories compared to species with faster life histories and higherr_max. Here, we posit that metabolic rate is related to the fast–slow life history continuum and the connection may be stronger for maximum metabolic rate and aerobic scope compared to resting metabolic rate. Specifically, we ask whether variation inr_maxor any of its component life‐history traits – age‐at‐maturity, maximum age, and annual reproductive output – explain variation in resting and maximum metabolic rates and aerobic scope across 84 shark and teleost species, while accounting for the effects of measurement temperature, measurement body mass, ecological lifestyle, and evolutionary history. Overall, we find a strong connection between metabolic rate and the fast‐slow life history continuum, such that species with faster population growth (higherr_max) generally have higher maximum metabolic rates and broader aerobic scopes. Specifically,r_maxis more important in explaining variation in maximum metabolic rate and aerobic scope compared to resting metabolic rate, which is best explained by age‐at‐maturity (out of the life history traits examined). In conclusion, teleosts and sharks share a common fast–slow physiology/life history continuum, with teleosts generally at the faster end and sharks at the slower end, yet with considerable overlap. Our work improves our understanding of the diversity of fish life histories and may ultimately improve our understanding of intrinsic sensitivity to overfishing.