Computational modelling of biological systems now and then: revisiting tools and visions from the beginning of the century.

Since the turn of the millennium, computational modelling of biological systems has evolved remarkably and sees matured use spanning basic and clinical research. While the topic of the peri-millennial debate about the virtues and limitations of 'reductionism and integrationism' seems less controversial today, a new apparent dichotomy dominates discussions: mechanistic versus data-driven modelling. In light of this distinction, we provide an overview of recent achievements and new challenges with a focus on the cardiovascular system. Attention has shifted from generating a universal model of human to either models of individual humans (digital twins) or entire cohorts of models representative of clinical populations to enable clinical trials. Disease-specific parametrization, inter-individual and intra-individual variability, uncertainty quantification as well as interoperable, standardized and quality-controlled data are important issues today, which call for open tools, data and metadata standards, as well as strong community interactions. The quantitative, biophysical and highly controlled approach provided by methods has become an integral part of physiological and medical research. methods have the potential to accelerate future progress also in the fields of integrated multi-physics modelling, multi-scale models, virtual cohort studies and machine learning beyond what is feasible today. In fact, mechanistic and data-driven modelling can complement each other synergistically and fuel tomorrow's artificial intelligence applications to further our understanding of physiology and disease mechanisms, to generate new hypotheses and assess their plausibility, and thus to contribute to the evolution of preventive, diagnostic and therapeutic approaches.This article is part of the theme issue 'Science into the next millennium: 25 years on'.