Increasing concentrations of anthropogenic greenhouse gases (GHGs) are known to be causing changes in global climate patterns, and will continue to do so for the foreseeable future. Our ability to predict future climatic states is still limited for a variety of reasons. Key among these reasons is our understanding of the coupled behaviour of the components of the Earth system. A research training programme GREENCYLCEII has scientific focus on the evaluation, improvement, and application of a range of different Earth System models (ESMs). This special issue brings together manuscripts from a range of GREENCYLCEII projects, broadly classed into data and model benchmarking, marine processes, terrestrial processes, high latitude feedbacks, and coupled modelling.