The tutorial will provide an overview of the fundamentals and of the state of the art in the area of brain-inspired Spiking Neural Networks (SNNs). The main topics to be covered include models, algorithms, and hardware implementations for Spiking Neural Networks (SNNs), along with applications, use cases, and future challenges. The tutorial will first discuss the technological landscape, including main players, applications, and use cases. Then, models for spiking neurons in SNNs will be presented by emphasizing the differences with respect to standard artificial neural networks and recurrent neural networks and by differentiating between deterministic and probabilistic models. Learning algorithms are presented next, discussing conversion-based, backpropagation-based, and probabilistic learning approaches, as well as bio-inspired local learning and adaptation. A presentation of hardware implementations of these models is provided by discussing conventional CMOS and post-CMOS technologies. Applications of these neuromorphic platforms will be then covered, before concluding with an outlook, including future challenges.