The technological breakthroughs of the last decade have given rise to a series of mobile devices (e.g. cell phones, medical implants, micro-sensors, etc.) which the proper functioning demands autonomous sources of energy. In this context, the vibration energy harvesters, based on piezoelectric effect, present themselves as a very appealing solution, since, when operating in a nonlinear regime, they are able to recover considerable amounts of energy in a wide band of frequencies outside a resonance. In order to better understand the efficiency of the electromechanical energy conversion processes on these systems, the present work conducts a detailed study of the bifurcations of a typical bistable energy harvester, which is characterized by a Duffing oscillator driven by a harmonic excitation. Different frequency bands and amplitude of excitation are considered in the analysis, showing that this type of harvester has extremely rich dynamics, with the presence of several mechanisms of bifurcation, hysteresis and chaos. In order to explore possible chaotic regimes in favor of the energy recovering process, the application of classical techniques of chaos control (OGY and Pyragas), to stabilize the system in unstable periodic orbits associated with high levels of energy, is also presented. The results show that the exploitation of the chaotic regime can be very useful in improving the efficiency of the system.