ATS methods provide an approach to fitting curves and surfaces to data using nonparametric regression when distributions are not necessarily Gaussian. First, a small amount of localaveraging(the“A”in ATS) is carried out, then a variance-stabilizingtransformationis applied (“T”), and finally the result issmoothed(“S”) using a nonparametric regression procedure. ATS methods are quite broad in terms of applications; in this article we show how they can be used for fitting a surface when the response is binary, for estimating density, and for estimating the spectrum of a time series. We also present some theoretical investigations that give guidance on how to choose the amount of averaging and how efficient the methods are.