The Paleoclimate Modelling Intercomparison Project (PMIP) has been set up to provide a mechanism for coordinating paleoclimate modelling and model evaluation activities, to understand the mechanisms of climate change and the role of climate feedbacks in these changes. PMIP is now in its fourth phase: PMIP4. Five PMIP4 experiments have been proposed within the framework of the CMIP6 exercise. Other periods and sensitivity experiments are also planned to assess climate sensitivity, changes in hydrology, long-term trends and interannual to millennium variability. This special issue is devoted to the description of the design of the PMIP4 experiments, of data syntheses to which model results can be compared, and to papers analysing single or multi-model results from PMIP4 and CMIP6 experiments. Papers can either be submitted to GMD (model and simulation descriptions, data syntheses in support of the experimental design or of model-data comparisons) or CP (in-depth analyses, multi-model analyses, model-data comparisons).