Second World War 1939–45
From:
http://www.awm.gov.au/atwar/ww2.htm
Almost a million Australians, both men and women, served in the Second World War. They fought in campaigns against Germany and Italy in Europe, the Mediterranean and North Africa, as well as against Japan in south-east Asia and other parts of the Pacific. The Australian mainland came under direct attack for the first time, as Japanese aircraft
bombed towns in north-west Australia and
Japanese midget submarines attacked Sydney harbour.
The Royal Australian Navy (RAN) participated in operations against Italy after its entry into the war in June 1940. A few Australians flew in the Battle of Britain in August and September but the Australian Army was not engaged in combat until 1941, when the 6th, 7th, and 9th Divisions joined Allied operations in the Mediterranean and North Africa.

At sea off Crete in the Mediterranean, 19 July 1940: Italian cruiser
Bartolomeo Colleoni under attack by HMAS
Sydney near Cape Spada.
AWM P01103.005
Following early successes against Italian forces, the Australians suffered defeat with the Allies at the hands of the Germans in Greece, Crete, and North Africa. In June and July 1941 Australians participated in the successful Allied invasion of Syria, a mandate of France and the Vichy government. Up to 14,000 Australians held out against repeated German attacks in the Libyan port of Tobruk, where they were besieged between April and August 1941. After being relieved at Tobruk, the 6th and 7th Divisions departed from the Mediterranean theatre for the war against Japan. The 9th Division remained to play an important role in the Allied victory at El Alamein in October 1942 before it also left for the Pacific. By the end of 1942 the only Australians remaining in the Mediterranean theatre were airmen serving either with 3 Squadron, Royal Australian Air Force (RAAF) or in the Royal Air Force (RAF).

North Africa, 6 January 1941: Australian troops advance into Bardia.
AWM 069221
Japan entered the war in December 1941 and swiftly achieved a series of victories, resulting in the occupation of most of south-east Asia and large areas of the Pacific by the end of March 1942. Singapore fell in February, with the loss of an entire Australian division. After the bombing of Darwin that same month, all RAN ships in the Mediterranean theatre, as well as the 6th and 7th Divisions, returned to defend Australia. In response to the heightened threat, the Australian government also expanded the army and air force and called for an overhaul of economic, domestic, and industrial policies to give the government special authority to mount a total war effort at home.
In March 1942, after the defeat of the Netherlands East Indies, Japan's southward advance began to lose strength, easing fears of an imminent invasion of Australia. Further relief came when the first AIF veterans of the Mediterranean campaigns began to come home, and when the United States assumed responsibility for the country's defence, providing reinforcements and equipment. The threat of invasion receded further as the Allies won a series of decisive battles: in the Coral Sea, at Midway, on Imita Ridge and the Kokoda Trail, and at Milne Bay and Buna.

Milne Bay, Papua, September 1942: a Bofors gun position manned by the 2/9th Light Anti-Aircraft Battery, Royal Australian Artillery, at Gili-Gili airfield. In the background a Kittyhawk is about to land.
Read more at the link.