This thesis examines how early warning signals perform when tested on climate systems thought to exhibit future tipping point behaviour. A tipping point in a dynamical system is a large and sudden change to the state of the system, usually caused by changes in external forcing. This is due to the state the system occupies becoming unstable, causing the system to settle to a new stable state. In many cases, there is a degree of irreversibility once the tipping point has been passed, preventing the system from reverting back to its original state without a large reversal in forcing. Passing tipping points in climate systems, such as the Amazon rainforest or the Atlantic Meridional Overturning Circulation, is particularly dangerous as the effects of this will be globally felt. Fortunately there is potential for early warning signals, designed to warn that the system is approaching a tipping point. Generally, these early warning signals are based on analysis of the time series of the system, such as searching for ‘critical slowing down’, usually estimated by an increasing lag-1 autocorrelation (AR(1)). The idea here is that as a system’s state becomes less stable, it will start to react more sluggishly to short term perturbations. While early warning signals have been tested extensively in simple models and on palaeoclimate data, there has been very little research into how these behave in complex models and observed data. Here, early warning signals are tested on climate systems that show tipping point behaviour in general circulation models. Furthermore, it examines why early warning signals might fail in certain cases and provides prospect for more ‘system specific indicators’ based on properties of individual tipping elements. The thesis also examines how slowing down in a system might affect ecosystems that are being driven by it.