The directionality of the radiated sound is very specific to each musical instrument. The underlying radiation mechanisms may, for instance, depend on the structure of the vibrating body (e.g., string and percussion instruments) or on the spatial distribution of the opening holes (e.g., bells and open finger holes for wind instruments). A good knowledge of the radiation pattern of instruments is essential for many applications, such as orchestration, room acoustics, microphone techniques for live sound and recording, and virtual acoustics. In the first part, we will review previous works on sound source radiation measurement and analysis, discuss the underlying acoustic principles, and try to identify common mechanisms of radiation in musical instruments. In the second part, we will illustrate various projects undertaken at IRCAM and dedicated to the measurement and modeling of the directivity of instruments, to the objective and perceptual characterization of room acoustics, and to the real-time synthesis of virtual source radiation for musical performances. For this latter, several approaches are discussed according to the underlying physical formalisms and associated electroacoustic setups (e.g., spherical loudspeaker arrays, wave field synthesis).