Archery Australia recognises two different types of crossbws, Target Crossbow and Field Crossbow.

Target Crossbows

Sporting Crossbow

Sporting crossbows are the commerical style crossbows available in either recurve or compound

In many states the ownership and use of crossbows is either banned (requiring a licence) or restricted. You should check the requirements in your state with your Archery Regional Governing Body. 

People who shoot crossbows are called "ARBALISTS".

Current WCSA rules