The cultivated strawberry (Fragaria × ananassa) is an allo-octoploid species, originating nearly 300 years ago from wild progenitors from the Americas. Since that time the strawberry has become the most widely cultivated fruit crop in the world, universally appealing due to its sensory qualities and health benefits. The recent publication of the first high-quality chromosome-scale octoploid strawberry genome (cv. Camarosa) is enabling rapid advances in genetics, stimulating scientific debate and provoking new research questions. In this forward-looking review we propose avenues of research toward new biological insights and applications to agriculture. Among these are the origins of the genome, characterization of genetic variants, and big data approaches to breeding. Key areas of research in molecular biology will include the control of flowering, fruit development, fruit quality, and plant-pathogen interactions. In order to realize this potential as a global community, investments in genome resources must be continually augmented.