A consequence of the description of the superfluid condensate in superfluid He or in superconductors as a single macroscopic quantum state is the quantization of circulation, resulting in quantized vortex lines. This book draws no distinction between superfluid He3 and He4 and superconductors. It examines theoretical and experimental progress in understanding of the vortex state in both superconductors and superfluids, from lectures given by both experimentalists and theoreticians, who gathered in Cargese for a NATO ASI. The peculiar features related to short coherence lengths, 2D geometry, high temperatures, disorder and pinning are discussed.