With the aim of facilitating the long-term transformation towards a sustainable future, the research field of sustainability transition has gained growing attention. A number of approaches have been proposed to understand or even manage the complex societal transition processes towards sustainable development. There are four popular approaches for sustainability transitions, i.e. the multi-phase concept, multi-level perspective, strategic niche management and transition management. However, there is a lack of studies to systematically review and critically reflect on these various approaches in this emerging field. This paper presents a holistic review of the four most common approaches, and more importantly identifies four critical challenges for the future studies on transition approaches. Consequently, the associated future research agenda is presented.