While multiple reasons make long-term demographic studies disproportionally valuable, much of their importance comes from the ability to detect and quantify rare events. We argue here that rare events can be critical for understanding important ecological and evolutionary processes. We highlight the additive or interactive nature of anthropogenic rare events with environmental rare events that may cause outsized changes in vital rates and therefore in population dynamics. Rare events may also generate complex responses in populations due to interactions between demographic processes and evolutionary responses. Complex, non-linear dynamics of populations may include threshold, extreme responses such as long transients, tipping points, regime shifts and collapse. When occurring locally, rare events may also exacerbate spatial heterogeneity with consequences for demographic processes. In sum, these effects represent substantial challenges for prediction, especially when considering the increase in the frequency of rare extreme events, and emphasise the need for long-term studies. Our perspective attempts to integrate the occurrence of rare events in variable environments and the consequences for the overall fitness, growth rates, and the spatial-temporal dynamics of populations.