This paper describes how constraint modelling can support design innovation. Furthermore, it lays out how constraints are employed in the construction and exploration of a modelis design space. The paper places this approach within the larger context of design exploration using computational and conceptual representations of design. Four general constraint types are identified and examples from several workshops and design studios are presented for each of the constraint types. The examples range from product design to structural design to fabrication issues in architecture. Based on a review of the literature the most common constraints are of geometric, topologic, functional, and quantitative type. Based on the case studies the paper describes how the different types of constraints can be used as design drivers and help in the exploration of solution space. In conclusion the paper identifies the addition of bi-directional properties to constraint modelling as the next challenge in improving the application of constraint modelling in design exploration. Furthermore, the paper demonstrates the necessity to develop better constraint models for cross domain design.