Both biomedical research and clinical practice rely on complex datasets for the physiological and genetic characterisation of human hearts in health and disease. Given the complexity and variety of approaches and recordings, there is now growing recognition of the need to embed computational methods in cardiovascular medicine and science for analysis, integration and prediction. This paper describes a Workshop on Computational Cardiovascular Science that created an international, interdisciplinary and inter-sectorial forum to define the next steps for a human-based approach to disease supported by computational methodologies. The main ideas highlighted were: (1) A shift towards human-based methodologies, spurred by advances in new in silico, in vivo, in vitro and ex vivo techniques and the increasing acknowledgement of the limitations of animal models. (2) Computational approaches complement, expand, bridge and integrate in vitro, in vivo and ex vivo experimental and clinical data and methods, and as such they are an integral part of human-based methodologies in pharmacology and medicine. (3) The effective implementation of multi- and inter-disciplinary approaches, teams, and training combining and integrating computational methods with experimental and clinical approaches across academia, industry and healthcare settings is a priority. (4) The human-based cross-disciplinary approach requires experts in specific methodologies and domains, who also have the capacity to communicate and collaborate across disciplines and cross-sector environments. (5) This new translational domain for human-based cardiology and pharmacology requires new partnerships supported financially and institutionally across sectors. Institutional, organisational and social barriers must be identified, understood and overcome in each specific setting.