The direction of outlyingness is crucial to describing the centrality of multivariate functional data. Motivated by this idea, we generalize classical depth to directional outlyingness for functional data. We investigate theoretical properties of functional directional outlyingness and find that it naturally decomposes functional outlyingness into two parts: magnitude outlyingness and shape outlyingness which represent the centrality of a curve for magnitude and shape, respectively. Using this decomposition, we provide a visualization tool for the centrality of curves. Furthermore, we design an outlier detection procedure based on functional directional outlyingness. This criterion applies to both univariate and multivariate curves and simulation studies show that it outperforms competing methods. Weather and electrocardiogram data demonstrate the practical application of our proposed framework. We further discuss an outlyingness matrix for multivariate functional data classification as well as plots for multivariate functional data visualization and outlier detection. The talk is based on joint work with Wenlin Dai.