We report on the development of anatomically accurate model of ventricles of the human heart. The model integrates our knowledge from a single cell to the whole organ and allows us to study mechanisms of cardiac arrhythmias in the human heart, where experimental interventions are very limited. We will present and discuss our recent research using this model. It includes studies of ventricular fibrillation during global ischaemia and quantification of the relative contributions of the hypoxia, acidosis and hyperkalemia on the changes in the fibrillation frequency and complexity. We have also studied arrhythmias which occur as a result of early after depolarizations (EADs). EADs occur in many forms of genetic defects such as the long QT syndrome or under the action of pharmacological agents as a result of cardiotoxicity. We also present our studies on the arrhythmias which occur due to fibrosis of cardiac tissue. We discuss importance of heterogeneity for the onset of the arrhythmias and recently found effect of attraction of sources of arrhythmia to the regions with a high degree of fibrosis. Finally we discuss possibilities of application of our approaches to clinic.