A phylogenetic tree of the Insecta orders.

 APTERYGOTA             | 
                        |
 Protura-------\        |
 Collembola-----|-------|
 Diplura-------/        |     /---Archaeognatha
                        |----|---Thysanura
                        |
------------------------|---------------------
PALEOPTERA              |
                        |----Ephemeroptera
          Odonata-------|
                        |
------------------------|---------------------
 NEOPTERA               |
                        |
                        |
 Phasmatodea--\         |
 Orthoptera----\        |
 Blattodea------|-------|-------|---Psocoptera
 Mantodea--/ / /  / / / | \     \-|---Mallophaga**
 Isoptera---/ /  / / /  |  \       \--Anoplura**
 Dermaptera--/  / / /   |   \
 Grylloblattodea / /    |    \
 Embioptera-----/ /     |     \---|---Thysanoptera
 Plecoptera------/      |          \-|--Homoptera
 Zoraptera------/       |             \--Hemiptera
                        |
                        |           /--Raphidioptera
                        |--|----|--|---Megaloptera
                        |  \     \--Neuroptera
                        |   \
                        |    \------Coleoptera
                        |
 Strepsiptera--\        |-------Hymenoptera
 Diptera--------|-----|-|
 Siphonaptera------|-/  | 
 Mecoptera--------/     |
                        |
 Trichoptera--------|---| 
 Lepidoptera-------/

The definitions for the terms are in their own special nodes, but sufficed to say that the tree starts at the top with the most "primitive" orders and progresses downwards to the more "advanced" orders. The placement of the orders on either side of the tree does not denote anything of importance, only to fit the orders in place.

**Quite a few classifications group Mallophaga (chewing lice) and Anoplura (sucking lice) into one order, Phthiraptera, but work done in 1978 by entomologists Kim and Ludwig shows that the orders are in fact distinct and should be listed separately.

Fundamentals of Entomology, Richard J. Elzinga, Fifth edition. Prentice Hall, New Jersey, 2000.
The Insects: An outline of entomology, second ed. Gullan, P.J. and P.S. Cranston. Blackwell Science, Great Britain, 2000.