Explaining biodiversity is a central focus in theoretical ecology. A significant obstacle arises from the Competitive Exclusion Principle (CEP), which states that two species competing for the same type of resources cannot coexist at constant population densities, or more generally, the number of consumer species cannot exceed that of resource species at steady states. The conflict between CEP and biodiversity is exemplified by the paradox of the plankton, where a few types of limiting resources support a plethora of plankton species. In this review, we introduce mechanisms proposed over the years for promoting biodiversity in ecosystems, with a special focus on those that alleviate the constraints imposed by the CEP, including mechanisms that challenge the CEP in well-mixed systems at a steady state or those that circumvent its limitations through contextual differences.