According to the neutral theory of molecular evolution, the evolutionary process is dominated by chance, in that the genetic variation observed in natural populations is shaped mainly by genetic drift. The stochastics of genetic drift is well understood in the classical Wright-Fisher model, where population size is constant, and gene reproduction is defined by a simplistic random descent algorithm. Yet what about more realistic models, where population size varies, and the population may also be structured? The standard approach to measure the magnitude of genetic drift in a structured population tries to find what is called an effective population size, loosely speaking the size of the Wright-Fisher population that would come closest to the one under consideration. There are different ways to make the concept of effective size exact. In a number of recent papers, the effective size for various population models was computed using an approach based on the coalescent approximation, with a linear time scale. For such an approximation to hold, a population should be well mixed and have a stable historical mean size. The most important aspects of the studies are: 1. geographically structured populations with a random environment; 2. the Wright-Fisher model with what has been called isolation by distance; 3. two-sex reproduction with polygamy. For each of these three types of models, the aim will be to establish the coalescent approximation, and translate the corresponding time scale into a formula for the effective size.