With the rising importance of powerful lasers in the scientific and industrial communities, material failure by interaction with intense laser radiation is today also a common event. In this status report we review the understanding of the physical processes that lead to laser-induced breakdown in bulk materials and on their surfaces. The roles and interplay of various mechanisms, which depend on material properties and the laser light intensity and frequency, are discussed. The experimental basis for electron avalanche behavior at optical frequencies is discussed in detail. Multiphoton ionization is briefly described. Tabulations of measured breakdown thresholds for transparent solids (bulk and surfaces), metal surfaces, liquids, and gases, and of multiphoton absorption coefficients, are presented. Experiments needed for further progress are discussed.