Computational modelling of cardiac function has evolved remarkably in the last decades and sees matured use spanning basic and clinical research. While the long-lasting debate about the virtues and limitations of 'reductionism and integrationism' has hushed, a new apparent dichotomy dominates discussions: mechanistic vs. data-driven modelling. In light of this distinction, we provide an overview of recent achievements and new challenges in modeling and simulating atrial arrhythmias. Attention has shifted from generating a universal model of the human to either models of individual humans (digital twins) or entire cohorts of models representative of clinical populations to enable in silico clinical trials. Disease-specific parameterisation, inter-individual and intra-individual variability, uncertainty quantification as well as interoperable, standardised, 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 in silico methods has become an integral part of physiological and medical research. In silico 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.