The paper provides an overview of functional data analysis (FDA), a statistical methodology for data that are in the form of functions, images, or shapes. FDA deals with the analysis and theory of such data, which can be recorded continuously or intermittently over time. The authors cover fundamental concepts such as mean and covariance functions, and introduce key techniques like functional principal component analysis (FPCA), functional linear regression, and clustering and classification methods. They discuss the challenges posed by the infinite-dimensional nature of functional data, including the need for dimension reduction and the presence of measurement errors. The paper also explores nonlinear approaches, such as time warping and manifold learning, and highlights the importance of smoothing methods and stochastic processes in FDA. The authors conclude with a discussion of future directions in the field.The paper provides an overview of functional data analysis (FDA), a statistical methodology for data that are in the form of functions, images, or shapes. FDA deals with the analysis and theory of such data, which can be recorded continuously or intermittently over time. The authors cover fundamental concepts such as mean and covariance functions, and introduce key techniques like functional principal component analysis (FPCA), functional linear regression, and clustering and classification methods. They discuss the challenges posed by the infinite-dimensional nature of functional data, including the need for dimension reduction and the presence of measurement errors. The paper also explores nonlinear approaches, such as time warping and manifold learning, and highlights the importance of smoothing methods and stochastic processes in FDA. The authors conclude with a discussion of future directions in the field.