In this paper, the current state of the art on shunt piezoelectric systems for noise and vibration control is reviewed. The core idea behind the operation of electronic shunt piezoelectric circuits is based on their capability of transforming the dynamic strain energy of the host structure, i.e., a smart beam or plate, into electric energy, using the properties of the direct piezoelectric phenomenon and sending this energy into the electronic circuit where it can be partially consumed and transformed into heat. For this purpose, transducers which are made by piezoelectric materials are used, since such materials present excellent electromechanical coupling properties, along with very good frequency response. Shunt piezoelectric systems consist of an electric impedance, which in turn consists of a resistance, an inductance or a capacitance in every possible combination. Several types of such systems have been proposed in the literature for noise or vibration control for both single-mode and multi-mode systems. The different types of shunt circuits provide results comparable to other types of control methods, as for example with tuned mass-dampers, with certain viscoelastic materials, etc. As for the hosting structure, several studies on beams and plates connected with shunt circuits have been proposed in recent literature. The optimization of such systems can be performed either on the design and placement of the piezoelectric transducers or on the improvement and fine-tuning of the characteristics of the system, i.e., the values of the resistance, the inductance, the capacitance and so on and so forth. There are several applications of shunt systems including among others, structural noise control, vibration control, application on hard drives, on smart panels etc. Last but not least, shunt circuits can be also used for energy harvesting in order to collect the small amount of energy which is necessary in order to make the system self-sustained.