Tail order is a notion for quantifying the strength of dependence in the tail of a joint distribution.It can account for a wide range of dependence,ranging from tail positive dependence to tail negative dependence.We will introduce theory and applications of tail order.Conditions for tail orders of copula families will be discussed,and they are helpful in guiding us to find suitable copula families for statistical inference.As applications of tail order,regression analysis will be demonstrated,using appropriately constructed copulas,that can capture the unique tail dependence patterns appear in a medical expenditure panel survey data.