I was asked in this talk to set the topic in the context of my career. After a degree in Mathematics I moved into Animal Behaviour starting with a PhD and postdoc at Oxford. Then I got a two-year lectureship at Glasgow and starting working with Peter Calow on how selection acts on life histories that are subject to constraints. We put our work together in a book, ‘The Physiological Ecology of Animals’, in 1986. There followed some difficult years for physiology, but in 2004 I was invited to talk on Life Histories to a Gordon Research Conference devoted largely to the new metabolic theory of ecology. That was the year that ‘Towards a metabolic theory of ecology’, was published, and I met one of the principal protagonists, Jim Brown, at the conference, and started a fruitful collaboration.    The metabolic theory of ecology (MTE) holds that the rate at which power can be delivered to the cells of bodies scales with body size  and temperature according to power laws. The scaling with body mass follows Kleiber’s law, scaling as M0.75. The scaling with temperature follows the Arrhenius equation. The result is that smaller organisms or organisms at higher temperatures can deliver power faster, per gram of organism, than larger organisms. So an organism’s metabolic rate sets the rate of resource allocation to the processes that regulate survival, growth, and reproduction. As a consequence, biological rates, such as birth rates, the rate of biomass production, developmental rates, and population growth rate, should scale allometrically to the − 1/4 power of body mass and the − 0.65 power of inverse absolute temperature. Biological times should scale to the + 1/4 power of body mass and the + 0.65 power of inverse temperature. A broad mass of data on plants, invertebrates, fish, reptiles, mammals, and birds generally supports MTE predictions, and there is at present no viable alternative framework within which to interpret these results. MTE provides a basic mechanistic explanation for why larger organisms and those with lower body temperatures grow more slowly, reproduce later, and are less productive when they do reproduce. My version of the explanation is that production and survival rates are selected to increase but are held back by constraints arising from the laws of physics, chemistry, and biology. MTE holds that productivity is limited by metabolic rate because of logistical constraints in supplying oxygen and other resources around the bodies of individual organisms, but there are unresolved problems with the theoretical formulation of this explanation. I will finish with a brief outline of another major outstanding life-history problem. Juvenile growth curves are generally sigmoid in shape: growth is initially nearly exponential, but it slows to near zero as the animal approaches maturity. The drop-off in growth rate is puzzling because, everything else being equal, selection favours growing as fast as possible. I will outline some existing attempts to find a solution to this puzzle.