Myelodysplastic syndrome (MDS) is considered a hematopoietic stem cell (HSC) disease, characterized by abnormal hematopoietic differentiation and a high propensity to develop acute myeloid leukemia (AML). It is mostly associated with advanced age, but also with prior anti-cancer therapy and inherited syndromes related to abnormalities in DNA repair. Recent technological advances have led to the identification of a myriad of frequently occurring genomic perturbations associated with MDS. These observations suggest that MDS and its progression to AML is a genomic instability disorder, resulting from a step-wise accumulation of genetic abnormalities. The notion is now emerging that the underlying mechanism of this disease may be a defect in one or more pathways that are involved in responding to or repairing damaged DNA. In this review, we will discuss these pathways in relationship to a large number of studies performed with MDS patient samples and MDS mouse models. Moreover, in view of our current understanding of how DNA damage response/repair pathways are affected by age in HSCs, we will also explore how this might relate to MDS development.