The COST Action ES1004 – European framework for online integrated air quality and meteorology modelling (EuMetChem) is focusing on a new generation of online integrated Atmospheric Chemical Transport (ACT) and Meteorology (Numerical Weather Prediction and Climate) models with two-way interactions between different atmospheric processes including chemistry (both gases and aerosols), clouds, radiation, turbulent mixing, emissions, meteorology and climate. Two major application areas of the integrated modelling are considered: (i) improved numerical meteorology and weather prediction (NWP) and chemical weather forecasting (CWF) with short-term feedbacks of aerosols and chemistry on meteorological variables, and (ii) two-way interactions between atmospheric pollution/composition and climate variability/change. The framework consists of 4 working groups namely: 1) Strategy and framework for online integrated modelling; 2) Interactions, parametrizations and feedback mechanisms; 3) Chemical data assimilation in integrated models; and 4) Evaluation, validation, and applications. Establishment of such an European framework (involving also key American experts) enables the EU to develop world class capabilities in integrated ACT/NWP-Climate modelling systems, including research, education and forecasting. This article provides an introduction to the EuMetChem goals and outcomes for this Special Issue "Coupled chemistry–meteorology modelling: status and relevance for numerical weather prediction, air quality and climate communities (SI of EuMetChem COST ES1004)" which collects key scientific papers of EuMetChem and its collaborators from different continents.