Items stolen from my checked baggage – compensation from the airline?

Any advice on the best approach to get compensation from an airline if items have been stolen from my checked in baggage? (Stupidly I didn't purchase travel insurance for this trip.)

Which airline?

Did you immediately report it to airline/ police at time of arrival?

I suspect most airlines will also have exclusion (similar to what Qantas has in section 7.4 of its Conditions of Carriage) which basically means that any items of substantial value (inc most electronic items) shouldn't be in checked baggae

In addition to moa's comments... It's also going to be rather difficult to prove that the (a) the item was in fact in your luggage to start with and (b) that the airline was responsible for it going missing. There are all sorts of disclaimers about checking items in and the main one is as moa stated, valuable items should always be kept in hand carry bags. 

Sister in Law had 200 pounds sterling worth of clothes stolen from her New York to Heathrow suitcase. She put in a claim with BA (Who she flew with), and got the money straight away. It isby all accounts an increasing problem, when flying in and out of the USA. I believe it may be that suitcase can not be locked/sealed and must be available be inspection at anytime during transit.

Get a "TSA lock". 

I believe that you are not allowed to lock or seal or suitcase, on flight in the USA. 

You are, but you need to use a TSA-compliant lock that allows you to lock the bag, yet it also allows TSA representatives to open the bag if required.

If you use another lock, it may be removed if the bag needs to be opened.

OHH well you learn something everyday.

Thank You good too know as we are thinking of going via the USA to UK and Europe next year.

You may have travel insurance through your credit card. I am not sure if you have to notify them before you travel to be valid though.