Systems and their environments must be understood in an integrated manner because any changes in the systems will affect their environments and vice versa in the ubiquitous open systems. Existing studies classify systems based on the diversity of their interactions and the systems' responses to changes in their environments. However, the uses of such classifications are limited. We attempt to address this limitation by using morphological analysis (MA) to identify, represent and characterise the general system–environment complex (SEC) and its components. The latter, called ‘dimensions’, and their respective manifestations, termed ‘variants’, are integrated into the MA representation to enable a holistic understanding of SECs in terms of six dimensions and 101 variants. The resultant representation and characterisation will help researchers identify potential research opportunities, demonstrated through the construction of a variants intersection matrix, and help develop practical principles for system design and evaluation. © 2021 John Wiley & Sons, Ltd.