The talk will introduce fundamental ideas of the analysis of time series of functions. Examples of such time series are yield curves and intraday return curves. Within the framework of functional data analysis, fundamental concept of long-run covariance, autocorrelations and their estimators will be introduced. Three specific inferential problems will be discussed: (1) testing if a functional time series is stationary, (2) testing if it is a functional weak white noise, (3) detecting change points in its mean structure in the presence of changing variability. An asymptotic framework as well as numerical implementation will be outlined.