The snapping turtles are members of the New World turtle family.

According Mlynarski's classification, there are only two full species in the snapping turtles:

1. Chelydridae family: Chelydra serpentina, the common snapper,
   with only four currently recognized subspecies
2. Macroclemys Temmincki , the alligator snapper, with only one subspecies in this group.

The full classification is as follows (Mlynarski, 1969):

Order: Testudines
Suborder : Cryptodira

• Superfamily: Chelydroidea
• Families:
  ( 1 )Chelydridae
  • Chelydra serpentina serpentina - the Common Snapping Turtle (Linneaeus 1758)
  • Chelydra serpentina osceola - the Florida Snapping Turtle (Stejneger 1818)
  • Chelydra serpentina rossignoni - the Mexican Snapping Turtle (Bocourt 1868)
  • Chelydra serpentina acutirostris - the South American
    (Equadorian) Snapping Turtle (Peters 1862)
  ( 2 )Macroclemys
  • Macroclemys temmincki - the Alligator Snapping Turtle (Troost 1835)

There is a group of turtles in Australia which makes up the genus Elseya with species:

• Elseya latisternum, (a species from the East Coast and around the Gulf of Carpentaria), is probably the most aggressive among australian turtles, and called " the saw-shelled snapper ".
• Elseya dentata (probably the largest of the australian Chelid turtles)
• Elseya novaeguinea (from New Guinea) are all also aggressive and try to bite whenever handled or molested. However, their only connection to the real snapping turtles, all included in Chelydridae, is just the common name.