Abstract: Varying-coefficient models are a useful extension of classical linear model. They are widely applied to economics, biomedicine, epidemiology, and so on. There are extensive studies on them in the latest three decade years. In this paper, many of models related to varying-coefficient models are gathered up. All kinds of the estimation procedures and theory of hypothesis test on the varying-coefficients model are summarized. From my opinion, some aspects waiting to study are proposed.

Key words: varying-coeffcient model, B-spline estimation, local estimation, generalized likelihood ratio test, sieve empirical likelihood