The engineering graduate of today will engage in a career which will span the middle of the twenty-first century, and beyond. They will work in a world which is increasingly more complex and uncertain than at any time before. This will require an integrated combination of technical knowledge and transferable skills and values, to a greater extent than ever before. This paper highlights the need for the contemporary engineering graduate to develop capacity to deal with increased uncertainty and complexity. It seeks to demonstrate how this can be achieved through developing key graduate attributes. These attributes may be promoted through suitable exposure to progressively more open-ended problems and activities across the programme. A number of exemplars are provided from two European chemical engineering programmes.