Inherited bone marrow failure syndromes (IBMFS) are a group of cancer-prone genetic diseases characterized by hypocellular bone marrow with impairment in one or more hematopoietic lineages. The pathogenesis of IBMFS involves mutations in several genes which encode for proteins involved in DNA repair, telomere biology and ribosome biogenesis. The classical IBMFS include Shwachman–Diamond syndrome (SDS), Diamond–Blackfan anemia (DBA), Fanconi anemia (FA), dyskeratosis congenita (DC), and severe congenital neutropenia (SCN). IBMFS are associated with high risk of myelodysplastic syndrome (MDS), acute myeloid leukemia (AML), and solid tumors. Unfortunately, no specific pharmacological therapies have been highly effective for IBMFS. Hematopoietic stem cell transplantation provides a cure for aplastic or myeloid neoplastic complications. However, it does not affect the risk of solid tumors. Since approximately 28% of FA, 24% of SCN, 21% of DBA, 20% of SDS, and 17% of DC patients harbor nonsense mutations in the respective IBMFS-related genes, we discuss the use of the nonsense suppression therapy in these diseases. We recently described the beneficial effect of ataluren, a nonsense suppressor drug, in SDS bone marrow hematopoietic cells ex vivo. A similar approach could be therefore designed for treating other IBMFS. In this review we explain in detail the new generation of nonsense suppressor molecules and their mechanistic roles. Furthermore, we will discuss strengths and limitations of these molecules which are emerging from preclinical and clinical studies. Finally we discuss the state-of-the-art of preclinical and clinical therapeutic studies carried out for IBMFS.