Learning disentangled representations in the imaging domain

•Tutorial about disentangled representation learning, i.e. learning how to separate out the underlying factors of variation.•Key concepts of machine learning and learning representations, causality, and domain shifts.•Detailed discussion of models that enforce disentanglement, their building blocks, and the existing metrics.•Comprehensive survey of disentanglement applications in medical domain•Analysis of disentanglement applications in medical imaging, discussing biases, models, and training setups.•A comprehensive listing of limitations, open challenges and existing opportunities in the field of disentanglement.