Vibration powered electrical generators typically feature a mass/spring resonant system to amplify small background vibrations. The compliance element in these resonant systems can become non-linear as a result of manufacturing limitations, physical operating constraints, or by deliberate design. The characteristics of mass/spring resonant systems with non-linear compliance elements are well known but they have not been widely applied within the field of energy harvesting. In this paper analysis of non-linear system behaviour using the harmonic balance method is presented, giving an insight into the potential benefits of non-linearities in energy harvesting applications. The design of a vibration powered energy harvester is reviewed and it is shown how the deliberate incorporation of non-linear behaviour within a design can be beneficial in improving magnetic loading and also in extending the range of frequencies over which the device can generate useful power.