In this paper, structural sound and vibration control using passive and semi-active shunt piezoelectric damping circuits is presented. A piezoelectric patch with an electrical shunt circuit is bonded to a base structure. When the structure vibrates, the piezoelectric patch strains and transforms the mechanical energy of the structure into electrical energy, which can be effectively dissipated by the shunt circuit. Hence, the shunt circuit acts as a means of extracting mechanical energy from the base structure. First, different types of shunt circuits (such as RL series circuit, RL parallel circuit and RL-C circuit), employed in the passive damping arrangement, are analyzed and compared. By using the impedance method, the general modelling of different shunt piezoelectric damping techniques is presented. The piezoelectric shunt circuit can be seen as additional frequency-dependence damping of the system. One of the primary concerns in shunt damping is to choose the optimal parameters for shunt circuits. In past efforts most of the proposed tuning methods were based on modal properties of the structure. These methods are used to minimize the response of a particular structural mode whilst neglecting the contribution of the other modes. In this study, a design method based on minimization of the sound power of the structure is proposed. The optimal parameters for shunt circuits are obtained using linear quadratic optimal control theory. In general, the passive shunt circuit techniques are an effective method of modal damping. However, the main drawback of the passive shunt circuit is that the shunt piezoelectric is very sensitive to tuning errors and variations in the excitation frequency. To overcome this problem, the pulse-switching shunt circuit, a semi-active continuous switching technique in which a RL shunt circuit is periodically connected to a bonded piezoelectric patch, is introduced as structural damping. The switch law for pulse-switching circuit is discussed based on the energy dissipation technique. Compared with a standard passive piezoelectric shunt circuit, the advantages of the pulse-switching shunt circuit is a small required shunt inductance, a lower sensitivity to environmental changes and easier tuning. Very low external power for the switch controller is required so it may be possible to extract this energy directly from the vibration of the structure itself. Numerical simulations are performed for each of these shunts techniques focusing on minimizing radiated sound power from a clamped plate. It is found that the RL series, RL parallel and pulse-switching circuits have basically the same control performance. The RL–C parallel circuit allows us to reduce the value of the inductance L due to the insertion of an external capacity C. However, the control performance will be reduced simultaneously. The pulse-switching circuit is more stable than RL series circuit with regard to structural stiffness variations. Finally, experimental results are presented using an RL series/parallel shunt circuit, RL-C parallel shunt circuit and pulse-switching circuit. The experimental results have shown that the vibration and noise radiation of a structure can be reduced significantly by using these shunt circuits. The theoretical and experimental techniques presented in this study provide a valuable tool for effective shunt piezoelectric damping.