Forms of wind-induced instability of structures are described, and two of these, typical of long bodies with bluff cross-sections, are selected for more detailed consideration. The first is vortex-induced bending oscillation, a type of resonant response to the periodic surface pressure loading caused by the discrete wake vortex street formed from the shear layers separating from the bluff cross-section. Oscillation phenomena are described, including capture of the vortex frequency by the structural response frequency over a discrete wind speed range and amplification and phase shift of the loading over this range. The second form is transverse galloping, arising from aerodynamic instability of the bluff cross-sectional shape, so that small-amplitude oscillations generate forces which increase the amplitudes to large values. Oscillation phenomena are described, including the occurrence at very nearly natural frequencies, and the relatively large amplitudes (compared to vortex-induced oscillations) increasing with wind speed beyond a critical wind speed dependent on the level o fstructural damping. Effects of body and wind parameters on both forms of oscillation are considered, and methods of analysis and suppression for susceptible structures are described. Some probable future requirements and prospects are considered.