Preparations for Exascale computing have led to the realization that future computing environments will be significantly different from those that provide Petascale capabilities. This change is driven by energy constraints, which is compelling architects to design systems that will require a significant re-thinking of how algorithms are developed and implemented. Co-design has been proposed as a methodology for scientific application, software and hardware communities to work together. This chapter gives an overview of co-design and discusses the early application of this methodology to High Performance Computing.