Between the 1930s and 50s, evolutionary biologists developed a successful theory of why organisms age, firmly rooted in population genetic principles. By the 1980s the evolution of aging had a secure experimental basis. Since the force of selection declines with age, aging evolves due to mutation accumulation or a benefit to fitness early in life. Here we review major insights and challenges that have emerged over the last 35 years: selection does not always necessarily decline with age; higher extrinsic (i.e., environmentally caused) mortality does not always accelerate aging; conserved pathways control aging rate; senescence patterns are more diverse than previously thought; aging is not universal; trade-offs involving lifespan can be 'broken'; aging might be 'druggable'; and human life expectancy continues to rise but compressing late-life morbidity remains a pressing challenge.