The entropy production rate of the climate is a topic of active study but ongoing confusion, spurred by the yet-unproven hypothesis that the climate system might be organising itself to maximise its entropy production rate and, more broadly, the potential of probing our climate from unorthodox simplifying perspectives. In this thesis, a re-examination of some fundamentals in this topic is offered.

Two main suggestions for a climate-relevant global entropy production rate have been established in the literature: one which focuses on non-radiative processes only (labelled 'material') and one which includes all radiative and non-radiative processes (labelled 'planetary'). Another physically-motivated entropy production rate is introduced and investigated here -- the transfer entropy production rate -- which distinguishes radiation according to the role it plays within the system, considering only entropy production due to those transfers of energy which occur within the climate. Various lines of reasoning and evidence point towards the new rate being physically meaningful, which is significant especially as it offers a re-interpretation of the entropy production optimisation hypothesis.

Next, the response of entropy production rates to changing climate conditions is investigated and the results used to verify a simple conceptual model capable of predicting the direction of the changes. The transfer and material entropy production rates are found to be significantly more responsive than the planetary rate to the climate's state and they both are able to resolve changes which surface temperature cannot: a simple solar radiation management scenario is found to be able to restore global average surface temperature but not the entropy production rates.

Finally, the measurement of the entropy production budget via radiation information in observational and GCM datasets is explored. A new method for accounting for entropy storage in the recently published CERES SYN1deg entropy flux dataset is demonstrated, which makes it possible to estimate the material and transfer entropy production rates from that dataset. This reveals that the transfer and material entropy production rates have increased in line with temperature over the past 20 years and that entropy production rates are higher in years with higher solar absorption. Furthermore, there is a hemispheric asymmetry of entropy production, with more occurring in the Northern hemisphere. The global mean material entropy production rate is 55.3 mW/m^2K and the transfer entropy production rate, 82.0 mW/m^2K in that dataset between March 2000 and February 2018.

As a whole, this investigation deepens our understanding of entropy production in the climate and offers new definitions, frameworks and observed patterns to stimulate further research.