In this article, we propose a new approach for facial expression recognition (FER) using deep covariance descriptors. The solution is based on the idea of encoding local and global deep convolutional neural network (DCNN) features extracted from still images, in compact local and global covariance descriptors. The space geometry of the covariance matrices is that of symmetric positive definite (SPD) matrices. By conducting the classification of static facial expressions using a support vector machine (SVM) with a valid Gaussian kernel on the SPD manifold, we show that deep covariance descriptors are more effective than the standard classification with fully connected layers and softmax. Besides, we propose a completely new and original solution to model the temporal dynamic of facial expressions as deep trajectories on the SPD manifold. As an extension of the classification pipeline of covariance descriptors, we apply SVM with valid positive definite kernels derived from global alignment for deep covariance trajectories classification. By performing extensive experiments on the Oulu-CASIA, CK+, static facial expression in the wild (SFEW), and acted facial expressions in the wild (AFEW) data sets, we show that both the proposed static and dynamic approaches achieve the state-of-the-art performance for FER outperforming many recent approaches.