Critical effects in semiclassical light scattering, in which the standard approximations break down, are associated with forward peaking, rainbows, glories, orbiting, and resonances. Besides giving rise to beautiful optical effects in the atmosphere, critical effects have important applications in many areas of physics. Their interpretation and accurate treatment, however, are difficult. This book deals with the theory of these critical effects. After a preliminary chapter posing the problem of critical effects, the next three chapters on coronae, rainbows, and glories, are written to be accessible to a broader audience of physicists. The main part of the book then describes the results obtained from the application of complex angular momentum techniques to scattering by homogeneous spheres. These techniques lead to practically usable asymptotic approximations, and to new physical insights into critical effects. A new conceptual picture of diffraction, regarded as a tunnelling effect, emerges. The final two chapters contain brief descriptions of applications to a broad range of fields including linear and nonlinear optics, radiative transfer, astronomy, acoustics, seismology, atomic, nuclear, and particle physics. This book intends to convey the basic concepts and physical interpretations that emerge from the new approach, rather than the complete formalism.