Functional differential equations are abstract generalizations of all kinds of differential equations with complex arguments and integro-differential equations with various delays, whose stability research plays an important role in modern scientific research. This paper discusses the stability of neutral functional differential equations, nonlinear functional differential equations and stochastic delay functional differential equations. Although the numerical methods used in different types of functional differential equations are similar, there are some differences. Either method is designed to provide a reliable theoretical guarantee for the researches on the stability of functional differential equations.