An ever-increasing amount of data is available in biomedical research. In MOLAB, years of joint work with medical doctors have led to the creation of big databases of medical data from patients of solid tumors and leukemias, as well as other diseases such as diabetes. We work with medical images (MRI and PET), flow cytometry, histopathology, genetic alterations, etc. These data are scrutinized using dimensionality reduction and techniques like Topological Data Analysis (TDA) or Machine Learning. We advocate preserving the interpretability and identifiability of our models and connect as much as possible the results to mechanistic modelling.