The winds of the hot, luminous, O, B, and WR stars are driven by the line-scattering of the star's continuum radiation flux. Several kinds of observational evidence indicate that such winds are highly structured and variable, and it seems likely that a root cause of this variability is the known strong instability of the line-driving mechanism. Initial dynamical models of the nonlinear evolution of this instability confirm that the wind indeed becomes highly structured, with large amplitude (~500 – 1000 km/s) shocks that separate high-speed rarefied flow from lower speed, dense shells. Remarkably, such variability can often have an intrinsic character, persisting even in the absence of explicit perturbation, and it now appears that this is a direct consequence of a degeneracy in the steady-state solutions for such models. However, recent work indicates that including scattering effects, which have so far been ignored in these pure-absorption models, might reduce or even break this steady-state solution degeneracy; through the “line-drag” effect, scattering can also reduce the strength of the instability, possibly rendering it an advective character for which wind variability now requires explicit perturbation from below. This review will examine the consequences of these ideas for understanding the likely nature of wind variability among the various kinds of early-type stars.