Biological neural networks are equipped with unique temporal dynamics and an inherent capability to continuously adapt through online learning, both enabling them to perform intelligent tasks unattainable yet by today’s AI systems. Next-generation computing technologies focus on power- and area-efficient architectures and learning systems that are inspired by the structure and the functioning principles of the brain. This talk will provide an overview of the state of the art in the area of brain-inspired Spiking Neural Networks (SNNs). The neuronal dynamics of spiking neurons and the learning algorithms for SNNs will be presented, with emphasis on the so-called Spiking Neural Unit (SNU). The SNU is a novel neuron formulation that translates the biologically-inspired neural dynamics into deep learning. Remarkably, these biological insights enabled SNU-based deep learning to even surpass the state-of-the-art performance while simultaneously enhancing the efficiency of AI systems. Finally, novel biologically-inspired online learning will be presented that is essential for low-power, accurate and reliable operation of brain-inspired computing.