Functional data analysis (FDA) refers to the statistical analysis of data samples consisting of random functions or surfaces, where each function is viewed as one sample element. In classical FDA, the random functions contained in the sample are considered to be independent, smooth, and square integrable. More recently, deviations from these assumptions have been intensively studied, for example, in functional time series analysis. FDA methodology is essentially nonparametric, utilizes smoothing methods and allows for flexible modeling. The underlying random processes generating the data are generally but not always assumed to be square integrable. A simplifying assumption that is often made is that they are (non-stationary) Gaussian processes.