Populations evolve through individuals branching. This holds true for plants, animals, or humans, but also for individuals in a more allegoric sense, from atoms splitting or DNA replicating to abstract entities like species or languages mutating or branching off into new species or languages. In probability theory the pattern behind such phenomena is studied under the heading of branching processes. If time is reversed and the population traced backwards, a sort of dual process is obtained. It is called a coalescent: instead of branching, family lines merge. Whereas branching has been studied under very broad conditions, coalescence has only been analysed under extremely simplified assumptions like discrete time, constant population size, or asexual reproduction. We purport to penetrate more general coalescents. But there are other retrospective aspects on population development than those of genealogy. An interesting question concerns how to discern extinction caused by a (more or less drastic) change in environment from extinction due to endogenic population fluctuation. Another topic is to determine the population size a number of generations back from knowledge of today's size. Apart from its general interest, this problem arises in modern molecular biology, where PCR technique is applied to amplify the amount of DNA, and then you wish to infer the original concentration.