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Causal machine learning (CML) has experienced increasing popularity in healthcare. Beyond the inherent capabilities of adding domain knowledge into learning systems, CML provides a complete toolset for investigating how a system would react to an intervention (e.g.\ outcome given a treatment). Quantifying effects of interventions allows actionable decisions to be made whilst maintaining robustness in the presence of confounders. Here, we explore how causal inference can be incorporated into different aspects of clinical decision support (CDS) systems by using recent advances in machine learning. Throughout this paper, we use Alzheimer's disease (AD) to create examples for illustrating how CML can be advantageous in clinical scenarios. Furthermore, we discuss important challenges present in healthcare applications such as processing high-dimensional and unstructured data, generalisation to out-of-distribution samples, and temporal relationships, that despite the great effort from the research community remain to be solved. Finally, we review lines of research within causal representation learning, causal discovery and causal reasoning which offer the potential towards addressing the aforementioned challenges.