Fine-mapping in genome-wide association studies aims to identify potentially causal genetic variants among a set of candidate variants that are often highly correlated with each other owing to linkage disequilibrium. A variety of statistical approaches are used in fine-mapping, almost all of which are based on a multiple regression framework to model the relationship between genotype and phenotype, while accommodating specific assumptions about the distribution of variant effect sizes and using different inference algorithms. Owing to their modelling flexibility and the ease of making inferential statements, these approaches are predominantly Bayesian in nature. Recently, these approaches have been improved by refining modelling assumptions, integrating additional information, accommodating summary statistics, and developing scalable computational algorithms that improve computation efficiency and fine-mapping resolution.