Here, we review the current genetic approaches for grass improvement and their potential for the enhanced breeding of new varieties appropriate for a sustainable agriculture in a changing global climate. These generally out-breeding, perennial, self-incompatible species present unique challenges and opportunities for genetic analysis. We emphasise their distinctiveness from model species and from the in-breeding, annual cereals. We describe the modern genetic approaches appropriate for their analysis, including association mapping. Sustainability traits discussed here include stress resistance (drought, cold and pathogeneses) and favourable agronomic characters (nutrient use efficiency, carbohydrate content, fatty acid content, winter survival, flowering time and biomass yield). Global warming will predictably affect temperature-sensitive traits such as vernalisation, and these traits are under investigation. Grass biomass utilisation for carbon-neutral energy generation may contribute to reduced atmospheric carbon emissions. Because the wider potential outcomes of climate change are unpredictable, breeders must be reactive to events and have a range of well-characterised germplasm available for new applications.