The ancient subject of eschatology, like its equally ancient metaphysical twin cosmogony, concerns some of the most fundamental questions of human nature. For most of history, discussions in these subjects have been completely speculative. In the last generation, physics has changed that situation. We are familiar with the detailed quantitative structure of the standard Big Bang model of cosmology. What about the other side of the coin? Starting with Richard Gott's 1993 Nature paper, a small group of theoretical physicists and astrophysicists have used the tools of mathematical physics to formulate and critique quantitative statements about the likely remaining lifetimes of civilization and of the human race. In the course of reviewing Willard Wells's 2009 book, Apocalypse When: Calculating How Long the Human Race Will Survive, we will survey this subfield beginning from its philosophical origins with Brandon Carter's relativity based "Doomsday Argument''.