In 1758 the Swedish botanist Carl Linnaeus placed all carnivorans known at the time into the group Ferae (not to be confused with the modern concept of Ferae which also includes pangolins) in the tenth edition of his book Systema Naturae.
He recognized six genera: Canis (canids and hyaenids), Phoca (pinnipeds), Felis (felids), Viverra (viverrids, herpestids, and mephitids), Mustela (non-badger mustelids), Ursus (ursids, large species of mustelids, and procyonids).
It wasn't until 1821 that the English writer and traveler Thomas Edward Bowdich gave the group its modern and accepted name.

Initially the modern concept of Carnivora was divided into two suborders: the terrestrial Fissipedia and the marine Pinnipedia.
Below is the classification of how the extant families were related to each other after American paleontologist George Gaylord Simpson in 1945:
Order Carnivora Bowdich, 1821
Suborder Fissipedia Blumenbach, 1791
Superfamily Canoidea G. Fischer de Waldheim, 1817
Family Canidae G. Fischer de Waldheim, 1817 – dogs
Family Ursidae G. Fischer de Waldheim, 1817 – bears
Family Procyonidae Bonaparte, 1850 – raccoons and pandas
Family Mustelidae G. Fischer de Waldheim, 1817 – skunks, badgers, otters and weasels
Superfamily Feloidea G. Fischer de Waldheim, 1817
Family Viverridae J. E. Gray, 1821 – civets and mongooses
Family Hyaenidae J. E. Gray, 1821 – hyenas
Family Felidae G. Fischer de Waldheim, 1817 – cats
Suborder Pinnipedia  Iliger, 1811
Family Otariidae J. E. Gray, 1825 – eared seals
Family Odobenidae J. A. Allen, 1880 – walrus
Family Phocidae J. E. Gray, 1821 – earless seals
Since then, however, the methods in which mammalogists use to assess the phylogenetic relationships among the carnivoran families has been improved with using more complicated and intensive incorporation of genetics, morphology and the fossil record.
Research into Carnivora phylogeny since 1945 has found Fisspedia to be paraphlyetic in respect to Pinnipedia, with pinnipeds being either more closely related to bears or to weasels.
The small carnivoran families Viverridae, Procyonidae, and Mustelidae have found to be polyphyletic: 
Mongooses and a handful of Malagasy endemic species are found to be in a clade with hyenas, which the Malagasy species being in their own family Eupleridae.

The African palm civet is a basal cat-like carnivoran.

The linsang is more closely related to cats.

Pandas are not procyonids nor are they are natural grouping.
The giant panda is a true bear while the red panda is a distinct family.

Skunks and stink badgers are placed in their own family, and are the sister group to a clade pertaining Ailuridae, Procyonidae and Mustelidae sensu stricto.

Below is a table chart of the extant carnivoran families and number of extant species recognized by various authors of the first and fourth volumes of Handbook of the Mammals of the World published in 2009 and 2014 respectively:
In 1758 the Swedish botanist Carl Linnaeus placed all carnivorans known at the time into the group Ferae (not to be confused with the modern concept of Ferae which also includes pangolins) in the tenth edition of his book Systema Naturae. He recognized six genera: Canis (canids and hyaenids), Phoca (pinnipeds), Felis (felids), Viverra (viverrids, herpestids, and mephitids), Mustela (non-badger mustelids), Ursus (ursids, large species of mustelids, and procyonids). It wasn't until 1821 that the English writer and traveler Thomas Edward Bowdich gave the group its modern and accepted name.
Initially the modern concept of Carnivora was divided into two suborders: the terrestrial Fissipedia and the marine Pinnipedia. Below is the classification of how the extant families were related to each other after American paleontologist George Gaylord Simpson in 1945:
Order Carnivora Bowdich, 1821
Suborder Fissipedia Blumenbach, 1791
Superfamily Canoidea G. Fischer de Waldheim, 1817
Family Canidae G. Fischer de Waldheim, 1817 – dogs
Family Ursidae G. Fischer de Waldheim, 1817 – bears
Family Procyonidae Bonaparte, 1850 – raccoons and pandas
Family Mustelidae G. Fischer de Waldheim, 1817 – skunks, badgers, otters and weasels
Superfamily Feloidea G. Fischer de Waldheim, 1817
Family Viverridae J. E. Gray, 1821 – civets and mongooses
Family Hyaenidae J. E. Gray, 1821 – hyenas
Family Felidae G. Fischer de Waldheim, 1817 – cats
Suborder Pinnipedia  Iliger, 1811
Family Otariidae J. E. Gray, 1825 – eared seals
Family Odobenidae J. A. Allen, 1880 – walrus
Family Phocidae J. E. Gray, 1821 – earless seals
Since then, however, the methods in which mammalogists use to assess the phylogenetic relationships among the carnivoran families has been improved with using more complicated and intensive incorporation of genetics, morphology and the fossil record. Research into Carnivora phylogeny since 1945 has found Fisspedia to be paraphlyetic in respect to Pinnipedia, with pinnipeds being either more closely related to bears or to weasels. The small carnivoran families Viverridae, Procyonidae, and Mustelidae have found to be polyphyletic: 
Mongooses and a handful of Malagasy endemic species are found to be in a clade with hyenas, which the Malagasy species being in their own family Eupleridae.
The African palm civet is a basal cat-like carnivoran.
The linsang is more closely related to cats.
Pandas are not procyonids nor are they are natural grouping. The giant panda is a true bear while the red panda is a distinct family.
Skunks and stink badgers are placed in their own family, and are the sister group to a clade pertaining Ailuridae, Procyonidae and Mustelidae sensu stricto.
Below is a table chart of the extant carnivoran families and number of extant species recognized by various authors of the first and fourth volumes of Handbook of the Mammals of the World published in 2009 and 2014 respectively:
Carnivora