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This set of extensive tutorial reviews and lectures focusses on the semi-classical and quantum aspects of percolation methods and their application to breakdown phenomena in disordered composite or granular materials. It sets out to connect - for the first time and in a coherent fashion - many recent theoretical and experimental advances in adjacent fields, such as the investigation of nonlinear current-voltage characteristics of 'quantum-dotted' materials or Zener breakdown in Mott or Anderson insulators. Last but not least, a final chapter explores the application of quantum percolation methods to the rapidly emerging field of quantum computing and communication.

Percolation (Statistical physics) --- Quantum theory --- Atomic Physics --- Physics --- Physical Sciences & Mathematics --- Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics. --- System theory. --- Quantum physics. --- Condensed matter. --- Condensed Matter Physics. --- Complex Systems. --- Numerical and Computational Physics, Simulation. --- Quantum Physics. --- Statistical Physics and Dynamical Systems. --- Mechanics --- Thermodynamics --- Lattice theory --- Statistical physics --- Statistical physics. --- Mathematical statistics --- Statistical methods --- Dynamical systems. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Statics --- Condensed materials --- Condensed media --- Condensed phase --- Materials, Condensed --- Media, Condensed --- Phase, Condensed --- Liquids --- Matter --- Solids