Clinical decision support systems (CDSSs) represent digital health tools applicable to important tasks within the clinical decision-making process. Training data-driven CDSSs requires extracting medical knowledge from the available information by means of machine learning. The analysis of the complex (possibly big or high-dimensional) training data allows knowledge relevant to be obtained for clinical decisions related to the diagnosis, therapy, or prognosis. This chapter is devoted to training CDSSs by machine learning based on complex data. Remarkable recent examples of CDSSs including those based on deep learning are recalled here. Principles, challenges, or ethical aspects of machine learning are discussed here in the context of CDSSs. Attention is paid to dimensionality reduction, deep learning methods for big data, or explainability of the data analysis methods. Data analysis issues are discussed also for two particular CDSSs on which the author of this chapter participated.