Equus ferus przewalskii is the closest wild relative of our domestic
horse,
Equus ferus caballus. (There is some disagreement in the scientific community about the separation of these two populations into two different
species, but currently the consensus is to treat Przewalski horses as a species (or, subspecies) separate from our domestic horses.)
Equus caballus no longer exists in the wild.
Feral populations of
Equus caballus exist in many places, notably in the western part of North America, but these horses are the descendants of domesticated horses brought to North America by Europeans.
Przewalski’s horses too became extinct in the wild in the middle of the last century due to hunting by humans, heightened military activity within their habitat, and competition for habitat with domesticated livestock, but have been reintroduced into their natural steppe habitat (from individuals kept in captivity and in zoos) in parts of Mongolia and China, as of 1993. Some have also been released in the Chernobyl area, and that herd is doing well, since the access to the area is still restricted. (A thank you to moeyz for the reference to Chernobyl.)
As noted in the article by liveforever, Przewalski's horses have two more chromosomes than Equus caballus, but nevertheless the two populations freely interbreed when given the opportunity, and produce fertile offspring. Geneticists hypothesize that some genetic material originally united in one pair of chromosomes in Equus caballus has split into a separate chromosome in the Przewalski's horse, but that the genetic material is similar enough nevertheless to permit successful reproduction across the two species.
Among the interesting facts which have been learned by close study of the two species is that our horses, Equus caballus, show much less variation in their Y chromosomes than in their X chromosomes. (This is also true of the domestic dog.) X and Y variation among Przewalski's horses are roughly equivalent. The hypothesis is that in domesticating both wolves and horses, early human beings found the females to be far easier and safer to keep than the males. Accordingly, a large number of mares were probably domesticated, but only a few stallions, who are far more dangerous and difficult to manage. The relatively smaller number of stallions in the breeding pool would account for the relative similarities in the Y chromosomes of the resultant population. That the wild stock does not show this differential supports that hypothesis.
For a discussion of the genetic details see Horse Domestication and Conservation Genetics of Przewalski's Horse, Lau et al
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Kingdom: Animalia
Phylum: Chordata
Class: Mammalia
Order: Perissodactyla
Family: Equidae
Genus: Equus
Subgenus: E. (Equus)
Species: E. ferus
Subspecies: E. f. przewalskii