Over the past 15 years climate tipping points (CTPs) – which are reached when change in a climate subsystem (the ‘tipping element’) becomes self-perpetuating independent of the original forcing and results in a regime shift to a new subsystem state – have emerged as a source of scientific and public concern. Some CTPs are estimated to be reachable within the 1.5-2oC Paris Agreement range, with many more accessible by the ~3-4oC of warming possible on current policy trajectories. Recent work has also hypothesised that CTPs could ‘cascade’ – with the impacts of triggering one tipping element sufficient to trigger the next and so on – resulting in an emergent global tipping point. However, much discussion relies on a tipping element characterisation that is now over a decade old, which itself was based on an expert elicitation exercise in 2005. Since then there have been substantial advances in our understanding of CTP dynamics based on results from coupled and offline models, observations, and palaeoclimate studies. The tipping cascade hypothesis has also not yet been rigorously tested, with the suggestion of 2oC as a global tipping point remaining speculative. Furthermore, CTP definitions are often inconsistent, with some purported globally-impactful CTPs more accurately represented as either localised CTPs or even threshold-free feedbacks. Here we undertake an updated review of CTPs based on a wide range of recent literature. We estimate ranges for each proposed element’s tipping threshold, timescales, and impact on global and regional warming, as well as if evidence exists for self-perpetuation, rate-dependence, or hysteresis. Each proposed element is then catalogued with reference to a clear tipping point definition, separating global ‘core’ and regional ‘impact’ tipping elements from threshold-free feedbacks. Our estimates confirm that current global warming (~1.2oC) already lies within the lower end of some CTP threshold ranges, and several CTPs become likely or possible within the 1.5-2oC Paris range. In further work we use these estimates to test the potential for and impact of tipping cascades in response to global warming scenarios using a stylised model.