Component analysis is a powerful tool to identify dominant patterns of interactions in multivariate datasets. In the context of fMRI data, methods such as principal component analysis or independent component analysis have been used to identify the brain networks shaping functional connectivity (FC). Importantly, these approaches are static in the sense that they ignore the temporal information contained in fMRI time series. Therefore, the corresponding components provide a static characterization of FC. Building upon recent findings suggesting that FC dynamics encode richer information about brain functional organization, we use a dynamic extension of component analysis to identify dynamic modes (DMs) of fMRI time series. We demonstrate the feasibility and relevance of this approach using resting-state and motor-task fMRI data of 730 healthy subjects of the Human Connectome Project (HCP). In resting-state, dominant DMs have strong resemblance with classical resting-state networks, with an additional temporal characterization of the networks in terms of oscillatory periods and damping times. In motor-task conditions, dominant DMs reveal interactions between several brain areas, including but not limited to the posterior parietal cortex and primary motor areas, that are not found with classical activation maps. Finally, we identify two canonical components linking the temporal properties of the resting-state DMs with 158 behavioral and demographic HCP measures. Altogether, these findings illustrate the benefits of the proposed dynamic component analysis framework, making it a promising tool to characterize the spatio-temporal organization of brain activity.