Transformative advances in deep learning, such as deep reinforcement learning, usually rely on gradient-based learning methods such as backpropagation through time (BPTT) as a core learning algorithm. However, BPTT is not argued to be biologically plausible, since it requires to a propagate gradients backwards in time and across neurons. Here, we propose e-prop, a novel gradient-based learning method with local and online weight update rules for recurrent neural networks, and in particular recurrent spiking neural networks (RSNNs). As a result, e-prop has the potential to provide a substantial fraction of the power of deep learning to RSNNs. In this presentation, we will motivate e-prop from the perspective of recent insights in neuroscience and show how these have to be combined to form an algorithm for online gradient descent. The mathematical results will be supported by empirical evidence in supervised and reinforcement learning tasks. We will also discuss how limitations that are inherited from gradient-based learning methods, such as sample-efficiency, can be addressed by considering an evolution-like optimization that enhances learning on particular task families. The emerging learning architecture can be used to learn tasks by a single demonstration, hence enabling one-shot learning.