After the end of World War II, Austria laid claim to the Italian province of South Tyrol, which was historically part of the old Austro-Hungarian Empire and retained a large population of ethnic Germans. This especially in light of Mussolini's attempt at fully Italianizing the region, which saw most German-Speaking South Tyroleans exiled to Nazi Germany, though most returned after the war. There were hopes that the end of the war would help guarantee that Austria and South Tyrol could be reunited, but the allies were worried that taking too much land from Italy (much of which had already been given to Yugoslavia, France, and the new Free Territory of Trieste) would increase the popularity of the communist party in the country. As such, the allies didn't agree to an immediate turnover nor a referendum, though the promise was made that Italy would grant the region greater self-governance.
While these were put in place, dissatisfaction with their situation and the influx of ethnic Italians lead many in South Tyrol to start a separatist movement by whatever means necessary.
Befreiungsausschuss Südtirol (The Committee for the Liberation of South Tyrol) or BAS began a series of bombing campaigns in the 1950's, initially only targeting relics of the fascist government and trying to avoid loss of life. However, things changed after June 12th, 1961- the Night of Fire- when the BAS blew up 37 pylons in an attempt to knock out power for the Bolzano industrial zone. Their goal was to bring South Tyrolean independence to global attention, which it did, but also resulted in many members being arrested and military and police presence in South Tyrol increasing.
This was what began the more violent phase of the separatist movement, which was unfortunately exacerbated by German and Austrian neo-nazis who infiltrated the BAS. Assassinations and ambushes were made throughout the 1960's, the most infamous of which were the Cima Vallona attacks on June 25, 1967. In all, the BAS terror campaign cost 21 lives, including 15 members of Italian security forces, two civilians, and four of their own members. They also did more to harm South Tyrol's chances for independence than anything. The question of self-determination vs. independence was discussed by the United Nations in 1961, but the terrorist attacks ultimately ensured it would be unsuccessful. The issue was finally settled in 1971 with a new Austro-Italian treaty that guaranteed a greater form of self-governance as an autonomous province, with the additional promise that Austria would not meddle in South Tyrol's affairs. This was deemed satisfactory by many and the BAS ultimately faded away.
Austria relinquished its claim to South Tyrol in 1992.