How should life expectancy be calculated? More generally, how should life - bles be estimated? Since John Graunt’s pioneering contribution, read before theRoyalSocietyofLondonat6p. m. onthe27thofFebruary1661,demog- phers have developed better and better methods. Some concerns were raised, including concerns about how to deal with heterogeneous populations p- lished in an article inDemography in 1979 that I wrote with Kenneth Manton and Eric Stallard. Yet, a few years ago nearly all demographers believed that as long as the underlying population and death counts were accurate, then lifetables could be reliably estimated. John Bongaarts and Gri? Feeney launched a revolutionary assault on this dogma. Two key contributions by them are reprinted in Part I of this mo- graph. Some very good demographers agreed, as least in part, with B- gaarts’ and Feeney’s radical argument that when death rates are changing, then tempo e?ects distort conventional calculations of life expectancy. Other very good demographers disagreed. So John Bongaarts and I brought some leading demographers together in a research meeting, co-sponsored by the Max Planck Institute for Demographic Research and the Population Co- cil and held in New York City on November 18 and 19, 2004. Many of the papers discussed at the workshop, generally after considerable revision, were published in Demographic Research in 2005 and 2006. Nine of these articles, in some cases somewhat revised, are published in this monograph: they are the ?rst seven chapters in Part II and the two chapters in Part III.