This article presents a summary of passive, semipassive, semiactive, and active control methods for schemes using harvested energy as the main source of energy to suppress vibrations via piezoelectric materials. This concept grew out of the fact that energy dissipation effects resulting from energy harvesting can cause structural damping. First, the existing equivalent electromechanical modeling methods are reviewed for vibration-based energy harvesters using piezoelectric transducers. Modeling of base excitation cantilever beam ranges from lumped to distributed parameter formulations. The commonly used electrical power conditioning circuits and their optimization are also summarized and discussed. The energy dissipation from harvesting induces structural damping, and this leads to the concept of purely passive shunt damping. This article reviews the literature on vibration control laws along the lines of purely passive, semipassive, semiactive, and active control. The classification of pervious results is built on whether external power is supplied to the piezoelectric transducers. The focus is placed on recent articles investigating semipassive and semiactive control strategies derived from synchronized switching damping. However, whether or not the harvested energy is large enough to satisfy a vibration suppression requirement has become an important topic of research but has not yet specifically been addressed in previous studies. Hence, this survey also reviews the possible control methods aiming for less control energy consumption and addresses the potential application for simultaneous vibration control and energy harvesting.