So the Italian Empire under Mussolini was pretty disorganized compared to the strategies of the Nazi Regime. As Mark Mazower notes, a central reason for this difference was Italy's lack of a large settler population, leading Mussolini to advocate for a different type of empire. The places that the Italians invaded (outside of Ethiopia and Libya in Africa) were those associated with the older territories of the Italian city-states (such as Croatia and Albania) or with the Roman Empire (Macedonia and Greece). The Italian army was able to secure some of this territory but unable to subdue large areas without the intervention of the German army. Again, Mazower observes that while much of this activity took place after 1940, Italy at this point was a junior partner in the Axis and unable to maintain its own distinct imperial ambitions without the aide of its often unwilling ally. Even Italy had trouble defending its African territories, leading again to the intervention of the German army in North Africa in late 1941/ early 1942.

See Mark Mazower, Hitler's Empire, esp. Chapter 5.

Before the war Italy had a colonial empire in Libya and East Africa, and annexed Albania in 1939. Italy grabbed a piece of southeastern France when it entered the war in 1940. It then invaded Egypt and Greece unsuccessfully, and was bailed out by Germany, leading to the North Africa Campaign and the Axis invasion and occupation of Yugoslavia and Greece, where Italy gained a lot of territory. The Axis eventually lost the North Africa Campaign, leading to the Allied invasion of Sicily and eventually mainland Italy in 1943, after which Italy signed an armistice with the Allies. (Though the Italian Campaign between the Allies and Germany continued until the end of the war). Italy also invaded and occupied British Somaliland in 1940, but in 1941 the British returned and not only liberated their colony but captured all of Italian East Africa. In Greece and Yugoslavia, there were armed insurgencies during the occupation, led mainly by communists, which continued until the German retreat from the Balkans in 1944-45. Italy contributed a large army to the Eastern Front which participated in Operation Barbarossa (a tactical victory) and the Battle of Stalingrad (a massive defeat, needless to say). Italy also conducted, with German support, a 2+ year siege of Malta which failed, and also was defeated in major naval battles including the devastating Pearl Harbor-style attack by the British on Taranto in 1940, as the Axis lost the battle for the Mediterranean.

Italy ended the war occupied by the Allies and lost its wartime conquests as well as its prewar colonial empire.