Vibration-based energy harvesting using piezoelectric materials have been investigated by several research groups with the aim of harvesting maximum energy and providing power to low-powered wireless electronic systems for their entire operational life. The electromechanical coupling effect introduced by the piezoelectric vibration energy harvesting (PVEH) mechanism presents modelling challenges. For this reason, there has been a continuous effort to develop different modelling techniques to describe the PVEH mechanism and its effects on the dynamics of the system. The overall aims of this thesis are twofold: (1) a thorough theoretical and experimental analysis of a PVEH beam or assembly of beams; (2) an in-depth analytical and experimental investigation of the novel concept of a dual function piezoelectric vibration energy harvester beam/tuned vibration absorber (PVEH/TVA) or 'electromechanical TVA' and its potential application to vibration control. The salient novel contributions of this thesis can be summarised as follows: (i) An in-depth experimental validation of a PVEH beam model based on the analytical modal analysis method (AMAM), with the investigations conducted over a wider frequency range than previously tested. (ii) The precise identification of the electrical loads that harvest maximum power and that induce maximum electrical damping. (iii) A thorough investigation of the influence of mechanical damping on PVEH beams. (iv) A procedure for the exact modelling of PVEH beams, and assemblies of such beams, using the dynamic stiffness matrix (DSM) method. (v) A procedure to enhance the power output from a PVEH beam through the application of a tip rotational restraint and the use of segmented electrodes. (vi) The theoretical basis for the novel concept of a dual function PVEH beam/TVA, and its realisation and experimental validation for a prototype device. A thorough experimental validation of a cantilever piezoelectric bimorph energy harvester without a tip mass is presented under random excitation. The study provided a deep insight into the effect of PVEH on the dynamics of the system for variations in electrical load. An alternative modelling technique to AMAM, based on the DSM, is introduced for PVEH beams. Unlike AMAM, the DSM is exact, since it is based on the exact solution to the bending wave equation. It also readily lends itself to the modelling of beams with different boundary conditions or assemblies of beams of different crosssections. AMAM is shown to converge to DSM if a sufficiency of modes is used. Finally, an in-depth theoretical and experimental investigation of a prototype PVEHbeam/TVA device is presented. This device comprises a pair of bimorphs shunted by R-L-C circuitry and can be used as a tuned mass damper (TMD) to attenuate a vibration mode of a generic structure. The optimal damping required by this TMD is generated by the PVEH effect of the bimorphs. Such a device combines the advantages of conventional mechanical and electrical TVAs, overcoming their relative disadvantages. The results demonstrate that the ideal degree of attenuation can be achieved by the proposed device through appropriate tuning of the circuitry, thereby presenting the prospect of a novel class of 'electromechanical' tuned vibration absorbers.