Associated vibrations in mechanical power transmission elements such as gears and bearings significantly contribute to the dynamic behavior of the system to which they belong. Most research in this field describes measurements and signal processing methods to determine the effect of some design modifications. However, the number of investigations that try to solve the problem from the design stage is much smaller. The following study presents a review of the trends in the analysis of vibrations of power transmission elements and their relationship to the use of systematic design methodologies in the principal power transmission elements. A revision is shown in design considerations to prevent mechanical vibrations or reduce them to acceptable levels. The effects in terms of improvement in reducing vibrations of the most important works that have taken into account the vibrations in design stages are shown. The results show the importance of considering the mechanical vibrations in the design of power transmission elements. Moreover, the analysis of the state of the art shows the areas to be investigated that contemplate the development or application of formal design methodologies that take into account mechanical vibrations.