Nonparametric function estimation based upon time-dependent data is a challenging problem to both the data analyst and the theoretician. This paper serves as an introduction to the problem and discusses some of the approaches that have been proposed for smoothing autocorrelated data. A principal theme will be accounting for correlation in the data driven choice of a function estimator's smoothing parameter. Data-driven smoothing is considered in various settings including probability density estimation, repeated measures data, and time series trend estimation. Both applications and theoretical issues are addressed, and some open problems will be discussed.