Cell fate decisions are tightly regulated by complex signalling networks. Disturbed signalling through these networks is prominent in disease development. To elucidate pathway contributions and effects of alterations to the regulation of proliferation, quiescence, senescence, and apoptosis, computational modelling has been essential. Modelling heterogeneity on different scales was shown to be important for cell fate prediction. In recent years, personalised models capturing signalling and cell fate decisions have been developed. Of special interest is the application of these models to predict the response to drugs. In this review, we highlight examples of mathematical models of signalling pathways that regulate disease-relevant cell fate decisions on the path to develop individualised patient models for optimal treatment prediction.