Many viruses are able to insert their genetic material into host chromosomes. Three kind of integration exist:
Mandatory integration
Viruses for which this is an obligatory event during viral replication. This is the cases for the retroviridae, pseudoviridae, metaviridae, some myoviridae and siphoviridae.
Integration of the viral DNA results in permanent insertion of the viral genome into the host chromosomal DNA, referred as a provirus in the case of retroviruses or prophage in the case of prokaryotic viruses.
Occasional integration
This kind of integration is not necessary for virus replication, but confers some advantages to the host/virus couple. It can facilitate long term asymptomatic infection of cells (latency),and also provide an advantage to the host cell. Many bacterial toxines are carried out by prophages for example
.
Endogenous viral elements (EVE) 
Viruses integrated long time ago and "fossilized" into a host genome, through a rare and sometimes accidental process. There are two kinds of endogenous viruses: endogenous retroviruses, and rare RNA virus integration.
Endogenous retro-viruses: Integrated viral genome can remain latent and be passively replicated along with the host genome and passed on to the cell's offspring. Host's environmental condition changes can however reactivate the virus leading to viral transcription and production of new infectious viruses (productive infection).
Retrovirus genomes that become integrated in the germline are referred as endogenous retroviruses (ERV) to distinguish them from horizontally transmitted, not passed on to host progeny, termed "exogenous" retroviruses. Hepadnaviridae have ben found also integrated inhost genome, notably in plants
Endogenous ssDNA viruses: SsDNA viruses like circoviridae which don't encode for an integrase have been found integrated in many genomes. It can happen also in plants: Geminivirus genome have been found in the tobacco genome.
Rare RNA virus integration:dsRNA, ssRNA(+) and ssRNA(-) viruses do not get reverse transcribed and are unable to integrate in host genome. Still Arenavirus reverse-transcribed genome has been detected in mice. Also Bornaviridae, filoviridae and Totiviridae sequences have been found integrated into several mammalian genome, and Rhabdoviridae in insect genomes indicating tat this event can occur although it's very rare.
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