This review organizes ideas on the evolution of life histories. The key life-history traits are brood size, size of young, the age distribution of reproductive effort, the interaction of reproductive effort with adult mortality, and the variation in these traits among an individual's progeny. The general theoretical problem is to predict which combinations of traits will evolve in organisms living in specified circumstances. First consider single traits. Theorists have made the following predictions: (1) Where adult exceeds juvenile mortality, the organism should reproduce only once in its lifetime. Where juvenile exceeds adult mortality, the organism should reproduce several times. (2) Brood size should macimize the number of young surviving to maturity, summed over the lifetime of the parent. But when optimum brood-size unpredictably in time, smaller broods should be favored because they decrease the chances of total failure on a given attempt. (3) In expanding populations, selection should minimize age at maturity. In stable populations, when reproductive success depends on size, age, or social status, or when adult exceeds juvenile mortality, then maturation should be delayed, as it should be in declining populations. (4) Young should increase in size at birth with increased predation risk, and decrease in size with increased resource availability. Theorists have also predicted that only particular combinations of traits should occur in specified circumstances. (5) In growing populations, age at maturity should be minimized, reproductive effort concentrated early in life, and brood size increased. (6) One view holds that in stable environments, late maturity, broods, a few, large young, parental care, and small reproductive efforts should be favored (K-selection). In fluctuating environments, early maturity, many small young, reduced parental care, and large reproductive efforts should be favored (r-selection). (7) But another view holds that when juvenile mortality fluctuates more than adult mortality, the traits associated with stable and fluctuating environments should be reversed. We need experiments that test the assumptions and predictions reviewed here, more comprehensive theory that makes more readily falsifiable predictions, and examination of different definitions of fitness.