Evolutionary processes are typically studied in populations where the total number of organisms does not change with time. This separation of ecological and evolutionary dynamics however does not hold for many rapidly evolving populations. Examples include the geographic expansions of invasive species and the growth of cancerous tumors. Ecological and evolutionary dynamics are strongly coupled in such populations, and this coupling dramatically affects the course of evolution. Specifically, I will show that (i) increased demographic stochasticity during geographic expansions severely constrains the types of viable social interactions, such as cooperation and mutualism, (ii) density-dependent natural selection at the front of expanding populations can significantly affect the patterns of genetic diversity and promote the evolution of cooperation, (iii) mutations damaging cancer cells alter the course of tumor progression and can be used as a possible therapeutic target.