The rise in human longevity is one of humanity's crowning achievements. Although advances in public health beginning in the 19th century initiated the rise in life expectancy, recent gains have been achieved by reducing death rates at middle and older ages. A debate about the future course of life expectancy has been ongoing for the last quarter century. Some suggest that historical trends in longevity will continue and radical life extension is either visible on the near horizon or it has already arrived; whereas others suggest there are biologically based limits to duration of life, and those limits are being approached now. In "inconvenient truths about human longevity" we lay out the line of reasoning and evidence for why there are limits to human longevity; why predictions of radical life extension are unlikely to be forthcoming; why health extension should supplant life extension as the primary goal of medicine and public health; and why promoting advances in aging biology may allow humanity to break through biological barriers that influence both life span and health span, allowing for a welcome extension of the period of healthy life, a compression of morbidity, but only a marginal further increase in life expectancy.