The physics of Anderson transitions between localized and metallic phases in disordered systems is reviewed. The term "Anderson transition" is understood in a broad sense, including both metalinsulator transitions and quantum-Hall-type transitions between phases with localized states. The emphasis is put on recent developments, which include: multifractality of critical wave functions, criticality in the power-law random banded matrix model, symmetry classification of disordered electronic systems, mechanisms of criticality in quasi-one-dimensional and two-dimensional systems and survey of corresponding critical theories, network models, and random Dirac Hamiltonians. Analytical approaches are complemented by advanced numerical simulations.1 A remarkable exception is the behavior of ξ in disordered wires of the chiral symmetry, see Eqs. (5.21), (5.22).