Myelodysplastic syndrome (MDS) is a clonal blood disorder characterized by ineffective hematopoiesis, cytopenias, dysplasia and an increased risk of acute myeloid leukemia (AML). With the growing availability of clinical genetic testing, there is an increasing appreciation that a number of genetic predisposition syndromes may underlie apparent de novo presentations of MDS/AML, particularly in children and young adults. Recent findings of clonal hematopoiesis in acquired aplastic anemia add another facet to our understanding of the mechanisms of MDS/AML predisposition. As more predisposition syndromes are recognized, it is becoming increasingly important for hematologists and oncologists to have familiarity with the common as well as emerging syndromes, and to have a systematic approach to diagnosis and screening of at risk patient populations. Here, we provide a practical algorithm for approaching a patient with a suspected MDS/AML predisposition, and provide an in-depth review of the established and emerging familial MDS/AML syndromes caused by mutations in the ANKRD26, CEBPA, DDX41, ETV6, GATA2, RUNX1, SRP72 genes. Finally, we discuss recent data on the role of somatic mutations in malignant transformation in acquired aplastic anemia, and review the practical aspects of MDS/AML management in patients and families with predisposition syndromes.