
The Hystricognathi are an infraorder of rodents, distinguished from other rodents by the bone structure of their skulls. The masseter medialis passes partially through the infraorbital foramen and connects to the bone on the opposite side. This, together with their lack of an infraorbital plate and the relative size of the infraorbital foramen, distinguishes hystricognaths from other rodent groups.

The blesmols, also known as mole-rats, or African mole-rats, are burrowing rodents of the family Bathyergidae. They represent a distinct evolution of a subterranean life among rodents much like the pocket gophers of North America, the tuco-tucos in South America, or the Spalacidae.

The genus Thryonomys, also known as the cane rats, is a genus of rodent found throughout Africa south of the Sahara, the only members of the family Thryonomyidae. They are eaten in some African countries and are a pest species on many crops. The family name comes from the Greek word thryon, meaning a "rush" or "reed".
Caviidae, the cavy family, is composed of rodents native to South America and includes the domestic guinea pig, wild cavies, and the largest living rodent, the capybara. They are found across South America in open areas from moist savanna to thorn forests or scrub desert. This family of rodents has fewer members than most other rodent families, with 19 species in 6 genera in 3 subfamilies.

Caviomorpha is the rodent infraorder or parvorder that unites all New World hystricognaths. It is supported by both fossil and molecular evidence. The Caviomorpha was for a time considered to be a separate order outside the Rodentia, but is now accepted as a genuine part of the rodents. Caviomorphs include the extinct Heptaxodontidae and extant families of chinchilla rats, hutias, guinea pigs and the capybara, chinchillas and viscachas, tuco-tucos, agoutis, pacas, pacaranas, spiny rats, New World porcupines, coypu and octodonts.

The family Chinchillidae is in the order Rodentia and consists of the chinchillas, the viscachas, and their fossil relatives. This family is restricted to southern and western South America, mostly living in mountainous regions of the Andes but one species living on plains. They are medium to large-sized rodents, weighing from 800 g (28 oz) to 8 kg (18 lb), with strong hind legs and large ears and a bushy tail. All species have thick, soft fur, which is considered valuable in some cultures.

The coypu, also known as the nutria, is a large, herbivorous, semiaquatic rodent. Classified for a long time as the only member of the family Myocastoridae, Myocastor is now included within Echimyidae, the family of the spiny rats. The coypu lives in burrows alongside stretches of water, and feeds on river plant stems. Originally native to subtropical and temperate South America, it has since been introduced to North America, Europe, Asia, and Africa, primarily by fur farmers. Although it is still hunted and trapped for its fur in some regions, its destructive burrowing and feeding habits often bring it into conflict with humans, and it is considered an invasive species.

The dassie rat is an African rodent found among rocky outcroppings. It is the only living member of its genus, Petromus, and family, Petromuridae. The name "dassie" means "hyrax" in Afrikaans, and the two animals are found in similar habitats. Petromus means "rock mouse" and dassie rats are one of many rodents sometimes called rock rats. The family and genus names are sometimes misspelled as Petromyidae and Petromys.

Dasyproctidae is a family of large South American rodents, comprising the agoutis and acouchis. Their fur is a reddish or dark colour above, with a paler underside. They are herbivorous, often feeding on ripe fruit that falls from trees. They live in burrows, and, like squirrels, will bury some of their food for later use.

The Dinomyidae are a family of South American hystricognath rodents: the dinomyids were once a very speciose group, but now contains only a single living species, the pacarana. Several of the extinct dinomyids were among the largest rodents known to date; these included the bison-sized Josephoartigasia monesi and the smaller Josephoartigasia magna. The dinomyids are thought to have occupied ecological niches associated with large grazing mammals due to their ability to compete with the native ungulates of South America. These large forms disappeared after the formation of a connection to North America. The modern pacarana is only modest in size, considerably smaller than the capybara.

Echimyidae is the family of neotropical spiny rats and their fossil relatives. This is the most species-rich family of hystricognath rodents. It is probably also the most ecologically diverse, with members ranging from fully arboreal to terrestrial to fossorial to semiaquatic habits. They presently exist mainly in South America; three members of the family also range into Central America. Species of the extinct subfamily Heteropsomyinae formerly lived on Cuba, Hispaniola, and Puerto Rico in the Antilles, probably until the arrival of Europeans. Some authorities consider the nutria from southern and central South America to be a part of this family.

Eocardia is an extinct genus of rodent from the Early to Middle Miocene of Argentina and Chile, South America. The 30 centimetres (12 in) long creature was related to guinea pigs and the capybara.

The Eocardiidae are an extinct family of caviomorph rodents from South America. The family is probably ancestral to the living family Caviidae, which includes cavies, maras, and capybaras and their relatives. McKenna and Bell (1997) divided eocardiids into two subfamilies, Luantinae for two of the oldest genera and Eocardiinae for remaining genera. Kramarz (2006) has recommended the abandonment of these subfamilies, as the genera placed in Luantinae appear to represent basal eocardiids, rather than a specialized side branch. The latter hypothesis had been proposed by Wood and Patterson (1959).

The greater cane rat is one of two species of cane rats, a small family of African hystricognath rodents. The cane rat lives by reed-beds and riverbanks in Sub-Saharan Africa. Cane rats can grow to nearly 60 cm (2.0 ft) in length and weigh a little less than 8.5 kg (19 lb). It has rounded ears, a short nose, and coarse bristly hair. Its forefeet are smaller than its hind feet, each with three toes.

Hutias are moderately large cavy-like rodents of the family Capromyidae that inhabit the Caribbean Islands. Twenty species of hutia have been identified but at least a third are extinct. Only Desmarest's hutia and the prehensile-tailed hutia remain common and widespread; all other extant species are considered threatened by the IUCN. Their larger relatives, the giant hutias of the family Heptaxodontidae, are entirely extinct.

The lowland paca, also known as the spotted paca, is a large rodent found in tropical and sub-tropical America, from east-central Mexico to northern Argentina, and has been introduced to Cuba and Algeria.

The mountain paca is a small burrow-dwelling rodent whose habitats are high altitude South American forests. Pacas are nocturnal, sedentary, and solitary animals with territorial tendencies. It eats mostly fruits and seeds. The mountain paca primarily inhabits higher Andean montane forest regions in Venezuela, Colombia, Ecuador, Peru and Bolivia.

The coypu, also known as the nutria, is a large, herbivorous, semiaquatic rodent. Classified for a long time as the only member of the family Myocastoridae, Myocastor is now included within Echimyidae, the family of the spiny rats. The coypu lives in burrows alongside stretches of water, and feeds on river plant stems. Originally native to subtropical and temperate South America, it has since been introduced to North America, Europe, Asia, and Africa, primarily by fur farmers. Although it is still hunted and trapped for its fur in some regions, its destructive burrowing and feeding habits often bring it into conflict with humans, and it is considered an invasive species.

Octodontidae is a family of rodents, restricted to southwestern South America. Fourteen species of octodontid are recognised, arranged in seven genera. The best known species is the common degu, Octodon degus.

The Old World porcupines, or Hystricidae, are large terrestrial rodents, distinguished by the spiny covering from which they take their name. They range over the south of Europe and the Levant, most of Africa, India, and the maritime Southeast Asia as far east as Flores. Although both the Old World and New World porcupine families belong to the infraorder Hystricognathi of the vast order Rodentia, they are quite different and are not particularly closely related.

A paca is a member of the genus Cuniculus of ground-dwelling, herbivorous rodents in South and Central America. It is the only genus in the family Cuniculidae. They are large rodents with dots and stripes on their sides, short ears, and barely visible tails. They are also referred to as "gibnuts" or "royal rats".
The pacarana is a rare and slow-moving hystricognath rodent indigenous to South America. Native Tupi people call it the pacarana because it is superficially similar to the paca, a different rodent which is not in the same family. The pacarana has a chunky body and is large for a rodent, weighing up to 15 kg (33 lb) and measuring up to 79 cm (31 in) in length, not including the thick, furry tail.

The dassie rat is an African rodent found among rocky outcroppings. It is the only living member of its genus, Petromus, and family, Petromuridae. The name "dassie" means "hyrax" in Afrikaans, and the two animals are found in similar habitats. Petromus means "rock mouse" and dassie rats are one of many rodents sometimes called rock rats. The family and genus names are sometimes misspelled as Petromyidae and Petromys.

The dassie rat is an African rodent found among rocky outcroppings. It is the only living member of its genus, Petromus, and family, Petromuridae. The name "dassie" means "hyrax" in Afrikaans, and the two animals are found in similar habitats. Petromus means "rock mouse" and dassie rats are one of many rodents sometimes called rock rats. The family and genus names are sometimes misspelled as Petromyidae and Petromys.

The rodent parvorder or infraorder Phiomorpha comprises several living and extinct families found wholly or largely in Africa. Along with the Anomaluromorpha and perhaps the †Zegdoumyidae, they represent one of the few early colonizations of Africa by rodents.

The Phiomyidae are a family of prehistoric rodents from Africa and Eurasia. A 2011 study placed Gaudeamus in a new family, Gaudeamuridae.

Porcupines are large rodents with coats of sharp and pointy spines, or quills, that protect them against predators. The term covers two families of animals: the Old World porcupines of family Hystricidae, and the New World porcupines of family Erethizontidae. Both families belong to the infraorder Hystricognathi within the profoundly diverse order Rodentia and display superficially similar coats of quills: despite this, the two groups are distinct from each other and are not closely related to each other within the Hystricognathi. It is the third largest living rodent in the world after the capybara and beaver.

A tuco-tuco is a neotropical rodent in the family Ctenomyidae. Tuco-tucos belong to the only living genus of the family Ctenomyidae, Ctenomys, but they include approximately 60 different species. The common name, "tuco-tuco" comes from the "tuc-tuc" sound they make while they dig their burrows.