It is common to have data being recorded continuously in a time interval or intermittently at several discrete time points for each subject or experimental unit. Both types are examples of functional data. Functional data analysis deals with theory and methods for the analysis of data in the form of functions. This talk provides a brief overview of functional data analysis, starting with the underlying statistical notions and some core techniques, the most popular of which is the functional principal component analysis. This talk then presents several developed methodologies with data applications, such as functional clustering, regression, prediction, and changepoint analysis. These statistical methods are broadly applicable to longitudinally recorded functional data.