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Complex source pulsed beams (CSPB) are exact solutions of the wave equation which can be modeled by a time-dependent source located at a complex coordinate point. With a proper choice of parameters, these wave fields are confined in beamlike fashion in transverse planes perpendicular to the propagation axis while confinement along the axis is due to temporal windowing. Because they have these properties, CSPBs are useful wave objects for generating and synthesizing highly focused transient fields and for local probing of a medium. Furthermore, CSPBs form a complete set of basis functions for a new exact angular spectrum expansion of source-excited time-dependent fields. This paper reviews the techniques pertaining to these applications and research directions.