The Italian Empire, whilst small compared to the other European empires, gradually expanded in the early 20th century. Italy added additional territory to the empire in Africa, most notably Libya, and later defeated Albania in the Balkans. But the most famous Italian battles came in the larger wars.
Battle of Vetori Venetto:
In WW1 the Italians joined the Entente in 1915. Whilst British and French armies held the front with Germany, the Italian army was left to defeat Austria-Hungary. The Italian Campaign, in northern Italy, began in 1915 and lasted until 1918. After the the rout of Caporetto in which hundreds of thousands of Italians surrendered, it seemed that the Italian Campaign might end with Austria-Hungary victorious.
However, the war was not over, and in 1918 the Italians could count on further reinforcements from Britain and France to begin a new advance from Vittorio Veneto. The majority of divisions at the Battle of Vetori Venetto were Italian troops, and at this battle they came up against the Austro-Hungarian army that had no additional German reinforcements. At this battle the Eighth Italian Army took Venetto, and maintained their advances into early November. During this period hundreds of thousands of Austro-Hungarian troops surrendered. As such, this was the battle that effectively won the Italian Campaign for Italy as an armistice duly followed. The postwar treaties dissolved Austria-Hungary, although the Italian Empire was not greatly expanded.
In the early 1940s the Italians advanced into Egypt, ensuring war with the British Empire. In the Battle of the Mediterranean among the more famous naval battles was that of the Battle of Taranto. To retain a greater advantage in the Mediterranean Sea the Royal Navy planned an aircraft carrier raid at the Italian naval base of Taranto.
It was here that a group of Royal Navy torpedo-bombers bombarded Italian battleships in port at Taranto. Three Italian battleships stationed at the port were decimated by the airstrike. The Italians had not expected it as Taranto was a shallow water port where it was doubted that torpedo bombs could be effective. But somehow the Royal Navy had pulled it off.
The Italian navy gradually began to recover from Taranto, and in 1941 sent out a fleet to intercept Allied Greek bound convoys. Off the coast of Cape Matapan these Italian ships were located by a Royal Navy fleet, supported by one aircraft carrier. The Battle of Matapan was another defeat for the Italian Navy as they lost three cruisers and a couple of destroyers. The Italian battleship Vetori Venetto was salvaged, but required further repairs when it returned to port.
Battle of El Alamein:
Although recalled as a British/German battle in North Africa, the Battle of El Alamein in fact included a more diverse range of troops. The British Eighth Army had a number of Commonwealth divisions, whilst the Afrika Korps was a combination of Italian and German divisions. It was the largest battle in North Africa with hundreds of thousands of troops included.
After their earlier victories the Afrika Korps advanced, but at El Alamein any remaining chance of victory evaporated. The British and Commonwealth troops outnumbered the Afrika Korps, and most essentially had twice the number of tanks at their disposal. In this battle their larger number of tanks ensured victory as the Afrika Korps retreated. With greater Allied reinforcements arriving the remaining troops of the Afrika Korps surrendered in 1943. The Italian Empire was thus on the brink of defeat as the Allied armies set sail for Sicily.
Those were a few of the more famous Italian battles. The defeat at El Alamein ensured the defeat of the Italian Empire. Once the Allies had taken Sicily the Italians ended the war with the Allies, and the empire was dissolved in the postwar period.