The chapter presents the results of an experimental study of hydrodynamics and diffusion combustion of jets flowing out of long tubes in the Reynolds number range 200-13,500 into air. The methods used in the experiments are visualization in the ultraviolet region, PIV, and hot-wire anemometry. The amplitude-phase structure of optical filters in systems of the Hilbert diagnostics of phase optical density fields in gaseous and condensed systems was used in this work. A possibility of visualization of disturbances in phase optical density fields with arbitrary amplitudes is demonstrated. Two geometries are studied: jet combustion in a stationary atmosphere and in a cross flow. Propane and hydrogen in a mixture with an inert diluent (CO 2) were used as fuels. In the isothermal jet stream, propane-butane mixture and Freon-22 are used. The main attention in the problem is paid to the mechanism of pipe and jet instability interaction, resulting in the vortex motion in several spatial regions. For critical Reynolds numbers in a pipe, the characteristic is the mechanism of two-stage instability caused by turbulent spot (puff) formation inside the pipe and vortex structure generation in the jet-mixing layer. These vortex structures (puff) exert a strong influence both on the isothermal jet and on the flame.