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Rare diseases (RDs) concern a broad range of disorders and can result from various origins. For a long time, the scientific community was unaware of RDs. Impressive progress has already been made for certain RDs; however, due to the lack of sufficient knowledge, many patients are not diagnosed. Nowadays, the advances in high-throughput sequencing technologies such as whole genome sequencing, single-cell and others, have boosted the understanding of RDs. To extract biological meaning using the data generated by these methods, different analysis techniques have been proposed, including machine learning algorithms. These methods have recently proven to be valuable in the medical field. Among such approaches, unsupervised learning methods via neural networks including autoencoders (AEs) or variational autoencoders (VAEs) have shown promising performances with applications on various type of data and in different contexts, from cancer to healthy patient tissues. In this review, we discuss how AEs and VAEs have been used in biomedical settings. Specifically, we discuss their current applications and the improvements achieved in diagnostic and survival of patients. We focus on the applications in the field of RDs, and we discuss how the employment of AEs and VAEs would enhance RD understanding and diagnosis.