I will begin the talk with a tutorial on functional data analysis. Then I will present two applications of deep neural networks (DNNs) to functional data. Traditional methods require dimension reduction via pre-selected basis expansions, which may not be optimal. We propose an adaptive approach using a DNN with a basis-layer, where hidden units act as basis functions through micro neural networks. This architecture focuses on relevant information, improving dimension reduction and outperforming other DNNs in classification and regression tasks. This approach requires fully or intensively observed functional data, so it is not suitable for longitudinal data, aka sparsely and irregularly observed functional data. Transformers are well suited to handle longitudinal data and we demonstrate this in the second part of the talk. *Based on joint work with Cynthia Juang, Jonas Mueller and Junwen Yao.