Having insight into the causal associations in a complex system facilitates decision making, e.g., for medical treatments, urban infrastructure improvements or financial investments. The amount of observational data grows, which enables the discovery of causal relationships between variables from observation of their behaviour in time. Existing methods for causal discovery from time series data do not yet exploit the representational power of deep learning. We therefore present the Temporal Causal Discovery Framework (TCDF), a deep learning framework that learns a causal graph structure by discovering causal relationships in observational time series data. TCDF uses attention-based convolutional neural networks combined with a causal validation step. By interpreting the internal parameters of the convolutional networks, TCDF can also discover the time delay between a cause and the occurrence of its effect. Our framework learns temporal causal graphs, which can include confounders and instantaneous effects. Experiments on financial and neuroscientific benchmarks show state-of-the-art performance of TCDF on discovering causal relationships in continuous time series data. Furthermore, we show that TCDF can circumstantially discover the presence of hidden confounders. Our broadly applicable framework can be used to gain novel insights into the causal dependencies in a complex system, which is important for reliable predictions, knowledge discovery and data-driven decision making.