I will discuss several examples from population genetics and adaptive dynamics where the probability for a transition between “equilibrium” states is very low. These situations can occur when stochastic environmental conditions create scenarios with alternate stable states that can only be invaded by mutations of large effect, for instance in scenarios with overlapping generations and lottery competition. In a similar vein, when mutations of small effect cause intermediate phenotypes with low fitness, transitions can be rare. Another type of transition involves feedback between the environment and the distribution of population phenotypes, for example in terms of the evolution of mating preferences in combination with the evolution of ecological specialization. Yet another scenario occurs when multiple independent mutations are required to cross an “adaptive valley”. This has parallels in ecological theory, for example with the invasion of novel habitats (e.g. zoonotic diseases). I will encourage discussion of how these different concepts and modes of analysis may be extended to situations with eco-evo feedbacks.