Agricultural production is unstable as a result of complex, dynamic and interrelated factors such as climate, markets and public policy that are beyond farmers' control. Farmers must therefore develop new farming systems incorporating innovations in objectives, organization and practices adapted to changing production contexts. As a consequence, agronomists have expanded the "farming system design" field of research. A variety of quantitative and qualitative design approaches have been developed to support the analysis of current farming systems and the design and evaluation of alternatives. A comprehensive literature assessment is lacking for this emerging field of agricultural science. Here we review 41 farming system design approaches using computer models. Our main findings are the following: (1) the reviewed literature do not make reference to the theoretical approaches from the field of design science. (2) Two categories of farming system approaches can be distinguished: optimisation approaches, and participatory and simulation-based approaches. These two categories are connected to two of the main design science theories. (3) For optimisation approaches, farming system design is mainly seen as a problem-solving process. Emphasis is placed on the computational exploration of the solution space by a problem-solving algorithm. (4) For participatory and simulation-based approaches, conceptualization of the design problem is central to the farming system design process. The subsequent exploration of the solution space relies on the creativity of humans. (5) Optimisation approaches, and participatory and simulationbased approaches are oriented towards the development of exploitative rather than exploratory innovations. Exploitative innovations involve the exploitation of available knowledge while exploration innovations build on knowledge created in the course of the design process.