When is median a better measure of a distribution than mean?

The majority of statistical methods conduct inference using the population mean as the parameter of interest. For example, the intuition that drives regression is that over time, values will eventually regress back to their overall mean. However, if the distribution is non-normal, such as if it is skewed, or if there are outliers, the median or another quantile might be a better central tendency measure to use. Separate models exist for quantile regression that adapt to such types of data.