Is it legal to use handheld radios to listen to airport frequencies in Australia?
An Aeronautical License issued by the Australian Communications and Media Authority (ACMA) is required in order to operate a handheld aviation-band VHF transceiver in Australia.


  An aeronautical licence is issued to authorise a station that:
  
  
  is not fixed to an aircraft; 
  is operated on aeronautical frequencies;
  is operated for purposes relating to the operation of an aircraft, or
  airport or aerodrome operations; and 
  in relation to an aircraft
  includes a mobile station operated on board the aircraft or on the
  ground in communication with aircraft. 
  
  
  An aeronautical licence is
  necessary to authorise the operation of stations providing:
  
  
  air traffic control services; 
  aerodrome radio information services;
  private company radiocommunications; and 
  other airport or aerodrome
  services.
  


Reference: ACMA

The Australian-based recreationalflying.com tutorial website may also provide more useful information.

(Note: This applies for a transceiver -- i.e. transmit &amp; receive -- rules may be different for receive-only).