Modern Reptiles consist of a number of Orders, Families, Genera & Species.

Order of Modern Reptiles are the Lizards (Suborder Sauria).
Modern Lizards.

Order of Modern Reptiles are the Snakes (Suborder Serpentes).
Modern Snakes.

Order of Modern Reptiles are the Turtles and Tortoises.
Modern Turtles & Tortoises (page not yet set up).

Order of Modern Reptiles are the Crocodilians (Order Crocodylia).
Modern Crocodiles (page not yet set up).

The following taxonomy listing was copied (with our thanks and appreciation) from:

Taxonomy of Class Reptilia
(to family level)
Prepared by Donald L. Blanchard
A slight variant on this article was originally published in The Cold Blooded News,
the newsletter of the Colorado Herpetological Society, Vol 26, #2, February, 1999.

Donald L. Blanchard's website address is: http://home.pcisys.net/~dlblanc/ReptiliaTax.html

Subclass Anapsida (Note 1)
Order Testudines (turtles)
Suborder Cryptodira
Superfamily Testudinoidea
Family Chelydridae (Snapping Turtles)
Family Emydidae (Pond Turtles/Box and Water Turtles)
Family Testudinidae (Tortoises)

Superfamily Trionychoidea
Family Dermatemydidae (River Turtles)
Family Kinosternidae (Mud and Musk Turtles)
Family Carettochelyidae (Pig-nose Turtles)
Family Trionychidae (Softshell Turtles)

Superfamily Chelonioidea
Family Cheloniidae (Sea Turtles)
Family Dermochelyidae (Leatherback Turtles)

Suborder Pleurodira
Family Pelomedusidae (Afro-American Sideneck Turtles)
Family Chelidae (Austro-American Sideneck Turtles)

Subclass Lepidosauria
Order Rhynchocephalia
Suborder Sphenodontida
Family Sphenodontidae (Tuataras)

Order Squamata ("scaled reptiles")
Suborder Sauria (lizards)
Infraorder Iguania
Family Agamidae (Agamas)
Family Chamaeleonidae (Chameleons)
Family Iguanidae (Iguanas and Spinytail Iguanas)
Family Corytophanidae (Casquehead Lizards)
Family Crotaphytidae (Collared and Leopard Lizards)
Family Hoplocercidae
Family Opluridae (Madagascar iguanids)
Family Phrynosomatidae (Earless, Spiny, Tree, Side-blotched and Horned Lizards)
Family Polychrotidae (Anoles)
Family Tropiduridae (Neotropical Ground Lizards)

Infraorder Gekkota
Family Gekkonidae (Geckoes)
Family Eublepharidae (Eyelid Geckoes)
Family Pygopodidae (Legless Lizards)
Family Dibamidae (Blind Lizards)

Infraorder Scincomorpha
Family Cordylidae (Spinytail Lizards)
Family Gerrhosauridae
Family Gymnophthalmidae (Spectacled Lizards)
Family Teiidae (Whiptails and Tegus)
Family Lacertidae (Wall Lizards)
Family Scincidae (Skinks)
Family Xantusiidae (Night Lizards)

Infraorder Diploglossa
Family Anguidae (Glass Lizards and Alligator Lizards; Lateral Fold Lizards)
Family Anniellidae (American Legless lizards)
Family Xenosauridae (Knob-scaled Lizards)

Infraorder Platynota (Varanoidea)
Family Helodermatidae (Gila Monsters)
Family Lanthanotidae (Earless Monitor lizards)
Family Varanidae (Monitor Lizards)

Suborder Serpentes (snakes)
Superfamily Typhlopoidea (Scolecophidia)
Family Anomalepidae (Dawn Blind Snakes)
Family Typhlopidae (Blind Snakes)
Family Leptotyphlopidae/Glauconiidae (Slender Blind Snakes)

Superfamily Henophidia (Boidea)
Family Aniliidae/Ilysiidae (Pipe Snakes)
Family Anomochilidae (Dwarf Pipe Snakes)
Family Boidae (Boas and Pythons)
Family Bolyeridae (Round Island Boas)
Family Cylindrophiidae (Asian Pipe Snakes)
Family Loxocemidae (Mexican Burrowing Pythons)
Family Tropidophiidae (Woodsnakes, Round Island "Boas ")
Family Uropeltidae (Short-tail Snakes)
Family Xenopeltidae (Sunbeam Snakes)

Superfamily Xenophidia (Colubroidea = Caenophidia)
Family Acrochordidae (File Snakes)
Family Atractaspididae (Mole Vipers)
Family Colubridae (Colubrids)
Family Elapidae (Cobras, Kraits, Coral Snakes)
Family Hydrophiidae (Sea Snakes)
Family Viperidae (Vipers and Pit Vipers)

Suborder Amphisbaenia (amphisbaenians)
Family Amphisbaenidae (Worm Lizards)
Family Trogonophidae (Shorthead Worm Lizards)
Family Bipedidae (Two-legged Worm Lizards)

Subclass Archosauria
Order Crocodylia
Suborder Eusuchia
Family Crocodylidae (Crocodiles)

Note 1: The taxonomic position of turtles is quite controversial at the present time. This classification represents the traditional, conservative view.
Source: Modified from The EMBL Reptile Database, EMBL (European Molecular Biology Laboratory), Heidelberg, Germany. (Maintained by Peter Uetz, University of Washington. Modified by dlb) Taken off the Web, at http://www.embl-heidelberg.de/~uetz/LivingReptiles.html.