With recent advances in learning algorithms, recurrent networks of spiking neurons are achieving performance competitive with standard recurrent neural networks. Still, these learning algorithms are limited to small networks of simple spiking neurons and modest-length temporal sequences, as they impose high memory requirements, have difficulty training complex neuron models, and are incompatible with online learning. Here, we show how `Forward-Propagation-Through-Time' (FPTT) learning combined with novel Liquid Time-Constant spiking neurons resolves these limitations. Applying FPTT to networks of such complex spiking neurons, we demonstrate online learning of exceedingly long sequences while outperforming current online methods and approaching or outperforming offline methods on temporal classification tasks. FPTT's efficiency and robustness furthermore enables us to train in an end-to-end fashion the first deep and performant spiking neural network for object localization and recognition, demonstrating for the first time the possibility of training large-scale complex spiking neural network architectures online and on long temporal sequences.