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Demand for alternative sources of energy has grown steadily on the world stage. And the concept of sustainability appears in full force to reduce the environmental degradation generated by this great energy consumption. In this sense, energy harvesting plays a predominant role in this scenario. Energy harvesting is the process by which energy from external sources such as solar, wind, vibrational, and others can be transformed into electrical energy. The kinetic energy that machines or organisms make available to the environment is called vibrational energy and can be transformed into electrical energy from piezoelectric materials. The objective of this paper is to present the process of vibrational energy harvesting and the main challenges for useful energy generation. Studies will be presented in the area containing nonlinearities and chaos in the power generator system from piezoelectric materials. These nonlinearities may be embedded in the material rigidity, electrical circuit coupling and the electrical circuit itself. The base excitation of the system can be harmonic, random and harmonic-random. [ABSTRACT FROM AUTHOR]