Over the past four decades, shrimp aquaculture has turned into a major industry providing jobs for millions of people worldwide especially in countries with large coastal boundaries. While the shrimp industry continues to expand, the sustainability of shrimp aquaculture has been threatened by the emergence of diseases. Diseases caused by single-stranded DNA containing viruses, such as infectious hypodermal and hematopoietic necrosis virus (IHHNV) and hepatopancreatic parvovirus (HPV), have caused immense losses in shrimp aquaculture since the early 1980s. In fact, the disease outbreak in the blue shrimp (Penaeus stylirostris) caused by IHHNV in early 1980s ultimately led to the captive breeding program in shrimp being shifted from P. stylirostris to the white shrimp (Penaeus vannamei), and today P. vannamei is the preferred cultured shrimp species globally. To date, four single-stranded DNA viruses are known to affect shrimp; these include IHHNV, HPV, spawner-isolated mortality virus (SMV) and lymphoidal parvo-like virus (LPV). Due to the economic losses caused by IHHNV and HPV, most studies have focused on these two viruses, and only IHHNV is included in the OIE list of Crustacean Diseases. Hence this review will focus on IHHNV and HPV. IHHNV and HPV virions are icosahedral in morphology measuring 20-22nm in size and contain a single-stranded DNA (ssDNA) of 4-6kb in size. Both IHHNV and HPV are classified into the sub-order Brevidensoviruses, family Densovirinae. The genome architecture of both viruses are quite similar as they contain two completely (as in IHHNV) or partially overlapping (as in HPV) non-structural and one structural gene. Histopathology and polymerase chain reaction (PCR)-based methods are available for both viruses. Currently, there is no anti-viral therapy for any viral diseases in shrimp. Therefore, biosecurity and the use of genetically resistant lines remains as the corner stone in the management of viral diseases. In recent years, gene silencing using the RNA interference (RNAi) approach has been reported for both IHHNV and HPV via injection. However, the delivery of RNAi molecules via oral route remains a challenge, and the utility of RNAi-based therapy has yet to be materialized in shrimp aquaculture.