Abstract: The tests for heteroscedasticity or varying dispersion in regewssion models are very important problems of statistical diagnostics. This paper systematically surveys the studying developments of the tests for heteroscedasticity or varying dispersion in general regression models, generalized regression models and regression models with random effects based on longitudinal data. The work done by us in recent years are introduced and some problems about heteroscedasticity or varying dispersion are introducted. Several problems to be resolved are suggested.