The modern view of caustics as the singularities of mappings performed by rays is set forth. The substantial progress which has recently been achieved in research on caustic fields can be credited to progress in the theory of the singularities of differentiable mappings (catastrophe theory). This theory has generated an exhaustive classification of the structurally stable caustics and of the corresponding standard diffraction integrals which describe the fields near caustics. The standard integrals can be used to construct both local and uniform asymptotic field representations in the presence of caustics. Asymptotic methods for describing the field have also been developed for penumbral caustics associated with edge catastrophes and for several other types of caustics which arise in wave problems in optics, acoustics, radio propagation, plasma physics, atomic physics, etc.