Internal gravity wave beams propagate in a form of ʻbeamʼ from a wave source in the atmosphere and the ocean. This beam solution is superposition of monochromatic wave solutions for a given propagation direction, and is an exact solution of Euler equations. In the present review article, we consider ʻ3-wave interactionʼ of these beams. The 3-wave interaction among monochromatic waves is well-known to occur, but their dynamics among wave beams has not been elucidated so far. According to recent theoretical studies, occurrence of instability due to 3-wave interaction among wave beams depends not only on their amplitudes but also on their ʻwidthʼ. We demonstrate this fact by numerical simulation of Euler equations.