Familial clustering of myelodysplastic syndromes (MDS) and acute myeloid leukemia (AML) can be caused by inherited factors. We screened 59 individuals from 17 families with 2 or more biological relatives with MDS/AML for variants in 12 genes with established roles in predisposition to MDS/AML, and identified a pathogenic germline variant in 5 families (29%). Extending the screen with a panel of 264 genes that are recurrently mutated in de novo AML, we identified rare, non-synonymous germline variants in 4 genes segregating with MDS/AML in an additional 2 families each. Somatic mutations are required for progression to MDS/AML in these familial cases. Using a combination of targeted and exome sequencing of tumor and matched normal samples from 26 familial MDS/AML cases and asymptomatic carriers, we identified recurrent frameshift mutations in the cohesin-associated factor PDS5B, co-occurrence of somatic ASXL1 mutations with germline GATA2 mutations, and recurrent mutations in other known MDS/AML drivers. Mutations in genes that are recurrently mutated in de novo AML were under-represented in the familial MDS/AML cases, although the total number of somatic mutations per exome was the same. Finally, clonal skewing of hematopoiesis was detected in 67% of young, asymptomatic RUNX1 carriers, providing a potential biomarker that could be used for surveillance in these high-risk families.