This review presents research from the past 15 years that has been motivated by the discovery of the bistability phenomenon in the turbulent wake dynamics of bluff bodies with rectangular bases. Works involving theory, experiment, numerical simulation, and modeling have been published on a broad scope encompassing the original laminar bifurcation; its evolution in the turbulent wake regime; the impact on the body aerodynamics; and the sensitivity of the wake asymmetry to geometry, freestream conditions, and flow control. The review aims to provide a unifying context for the bistability phenomenon and evaluate its contribution to the aerodynamic performance of bluff bodies relevant to a wide majority of land vehicles and some naval superstructures.