Since the origin of life, new species have kept arising while others were disappearing. The new extinction crisis we are now facing, the sixth one, is mainly due to humans. Habitat loss, introduction of exotic species, pollution are the most important current causes of extinction. Once a species has started to decline, demographical, or environmental stochastic processes may trap it in a vortex towards extinction. The study of rare species gives new insights into the dynamics of these processes and the evolutionary processes involved. Indeed, there is also an "evolutionary vortex" that may lead to extinction. A species which is highly adapted to a particular habitat is more vulnerable to habitat loss than a generalist species. As patches of suitable habitats disappear, natural selection in such species favors genes that decrease dispersal propensity. This, in turn, will usually select for increased local adaptation. Natural selection might also lead to the maintenance of mating systems such as self-incompatibility, that are particularly deleterious in small populations of rare species.