Regression analysis is one of the most commonly used techniques in statistics. When the dimension of independent variables is high, it is difficult to conduct efficient nonparametric analysis straightforwards from the data. As an important alternative to the additive and other nonparametric models, varying-coefficient models can reduce the modeling bias and avoid “”curse of dimensionality”” significantly. In addition, the coefficient functions can easily be estimated via a simple local regression. Based on local polynomial techniques, we provide the asymptotic distribution for the maximum of the normalized deviations of the estimated coefficient functions away from the true coefficient functions. Using this result and the pre-asymptotic substitution idea for estimating biases and variances, simultaneous confidence bands for the underlying coefficient functions are constructed. An important question in the varying coefficient models is if an estimated coefficient function is statistically significantly different from zero or a constant. Based on newly derived asymptotic theory, a formal procedure is proposed for testing whether a particular parametric form fits a given data set. Simulated and real-data examples are used to illustrate our techniques.