Vibration energy harvesting typically involves a mechanical oscillatory mechanism to accumulate ambient kinetic energy, prior to the conversion to electrical energy through a transducer. The convention is to use a simple linear mass-spring-damper oscillator with its resonant frequency tuned towards that of the vibration source. In the past decade, there has been a rapid expansion in research of vibration energy harvesting into various nonlinear vibration principles such as Duffing nonlinearity, bistability, parametric oscillators, stochastic oscillators and other nonlinear mechanisms. The intended objectives for using nonlinearity include broadening of frequency bandwidth, enhancement of power amplitude and improvement in responsiveness to non-sinusoidal noisy excitations. However, nonlinear vibration energy harvesting also comes with its own challenges and some of the research pursuits have been less than fruitful. Previous reviews in the literature have either focussed on bandwidth enhancement strategies or converged on select few nonlinear mechanisms. This article reviews eight major types of nonlinear vibration energy harvesting reported over the past decade, covering underlying principles, advantages and disadvantages, and application-specific guidance for researchers and designers.