Many studies have shown that rapid evolution is common and can affect various ecological dynamics. However, the original studies on eco-evolutionary dynamics tended to focus on rapid evolution in predator-prey interactions. Here I introduce our recent theoretical studies on rapid evolution in the context of competition. Rapid evolution can promote species coexistence via (i) intraspecific adaptation load where adaptation to intraspecific sexual and social interactions reduces population growth and (ii) relative nonlinearity where competitively dominant species (with smaller R^*) causes population cycles whereas competitively inferior species (with larger R^*) stabilizes population cycles by eco-evolutionary feedbacks. In addition, I explain how to define eco-evolutionary niche and competitive ability differences of Modern Coexistence Theory (MCT) based on invasibility and discuss future challenges.