Virus latency (or viral latency) is the ability of a pathogenic virus to lie dormant (latent) within a cell, denoted as the lysogenic part of the viral life cycle. A latent viral infection is a type of persistent viral infection which is distinguished from a chronic viral infection. A latent infection is a phase in certain viruses' life cycles in which after initial infection, virus production ceases. However, the virus genome is not fully eradicated. The result of this is that the virus can reactivate and begin producing large amounts of viral progeny without the host being infected by new outside virus, denoted as the lytic part of the viral life cycle, and stays within the host indefinitely.
Virus latency is not to be confused with clinical latency during the incubation period when a virus is not dormant.
Episomal latency 
Episomal latency refers to the use of genetic episomes during latency. In this type, viral genes are floating in the cytoplasm or nucleus as distinct objects, both as linear or lariat structures. Episomal latency is more vulnerable to ribozymes or host foreign gene degradation than provirus latency.
One example is Herpes Virus family, Herpesviridae, all of which establish latent infection. Herpes virus include Chicken-pox virus and Herpes simplex viruses (HSV-1, HSV-2), all of which establish episomal latency in neurons and leave linear genetic material floating in the cytoplasm. The Gammaherpesvirinae subfamily is associated with episomal latency established in cells of the immune system, such as B-cells in the case of Epstein-Barr Virus.
A provirus is a virus genome that is integrated into the DNA of a host cell.
Advantages include automatic host cell division results in replication of the viruses gene, and the fact that it is near impossible to remove an integrated provirus from an infected cell without killing the cell.
Disadvantages include the need to enter the nucleus (and the need for packaging proteins that will allow for that) and increased difficulty in maintaining the latency.
Maintaining latency 
Both proviral and episomal latency may require maintenance for continued infection and fidelity of viral genes. Latency is generally maintained by viral genes expressed primarily during latency. Expression of these latency-associated genes may function to keep the viral genome from being digested by cellular ribozymes or being found out by the immune system. Certain viral gene products (RNA transcripts such as non-coding RNAs and proteins) may also inhibit apoptosis or induce cell growth and division to allow more copies of the infected cell to be produced.
An example of such a gene product is the Latency Associated Transcripts (LAT) in Herpes simplex virus, which interfere with apoptosis by downregulating a number of host factors, including Major Histocompatibility Complex (MHC) and inhibiting the apoptotic pathway.
A certain type of latency could be ascribed to the endogenous retroviruses. These viruses have incorporated into the human genome in the distant past, and are now passed through reproduction. Generally these types of viruses have become highly evolved, and have lost the expression of many gene products. Some of the proteins expressed by these viruses have co-evolved with host cells to play important roles in normal processes.
While viral latency exhibits no active viral shedding nor causes any pathologies or symptoms, the virus is still able to reactivate via external activators (i.e. sunlight, stress) to cause an acute infection. In the case of Herpes simplex virus, which generally infects an individual for life, a serotype of the virus reactivates occasionally to cause cold sores. Although the sores are quickly resolved by the immune system, they may be a minor annoyance from time to time. In the case of varicella zoster virus, after an initial acute infection (chickenpox) the virus lies dormant until reactivated as herpes zoster.
More serious ramifications of a latent infection could be the possibility of transforming the cell, and forcing the cell into uncontrolled cell division. This is a result of the random insertion of the viral genome into the hosts own gene and expression of host cellular growth factors for the benefit of the virus. A famous event of this actually happening with gene therapy through the use of retroviral vectors is the Necker Hospital in Paris, where 20 young boys received treatment for a genetic disorder, after which 5 developed leukemia-like syndromes .
In the field of HIV research, proviral latency in specific long-lived cell types is the basis for the concept of one or more viral reservoirs, referring to locations (cell types or tissues) characterized by persistence of latent virus. Specifically, the presence of replication-competent HIV in resting CD4-positive T cells, allows this virus to persist for years without evolving despite prolonged exposure to antiretroviral drugs. This latent reservoir of HIV may explain the inability of antiretroviral treatment to cure HIV infection.
See also 
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