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Generation of intense terahertz and infrared radiation with a high-intensity laser pulse is studied for interaction with mass-limited and gas targets. In the first case, fast and strongly non-stationary processes are initiated, which are characterized by considerable charge separation. A laser pulse of relativistic intensity incident normally at a mass-limited target can induce a simultaneous motion of all electrons from the target in the longitudinal direction (along the laser beam axis) due to the Lorentz force. This force accelerates electrons to relativistic velocities. As a result, a relativistic electron bunch can be formed and its electron density can be about solid target density. For relativistic electron bunch formation, the laser pulse amplitude should be larger than some threshold, which is determined by the material and geometry of the target. During interaction, ions of the target cannot move considerably from their initial position because of high inertia. Due to strong Coulomb field, after some time, a part of relativistic electrons turns back and returns to their initial position. Because of gained velocity, they oscillate around the ions. In this case, radiated pulse can contain several cycles of oscillations, its frequency depends on the system parameters and can belong to the terahertz or infrared bands. It is shown that the temporal profile of radiation depends on the laser pulse amplitude and duration, electron density of the target and its geometry. The amplitude of the radiation can be at the relativistic level for modern petawatt laser systems. Several analytical models are proposed for this process and studied. In the second case, relatively long pulses of terahertz or infrared bands can be generated with a wakefield formed by a laser pulse in a gas medium. For increasing the interaction, a density modulated plasma can be used. Characteristics of radiation generated during this process such as polarization, frequency, amplitude, etc. are studied. Here also, analytical model is considered for generation of terahertz or infrared radiation.