The Italian Campaign had as strategic motivation, on the one hand, the possibility of knocking Italy - a major Axis power - out of the war, and secondly, to attract German military resources from other theaters of operations on a secondary front.
The Allied Invasion of Sicily was carried out in July - August 1943. The British Eighth Army, under General Bernard Montgomery, and the U.S. Seventh Army, led by General George S. Patton, landed in the south of the island. The Italian and German forces defending Sicily resisted especially around Mount Etna but were compelled to evacuate the island in the face of the Allied pressure after about a month.
Shortly afterward, in September 1943, the Allied Invasion of Italy took place. Immediately after the Allied landings, Italy signed an armistice with the Allies, which prompted the Germans to occupy the country. The Anglo-American forces landed in the south of mainland Italy in several places, but at Salerno, near Naples, met the strongest German resistance. The Allied air and naval support proved decisive in the end, and the Germans began to retreat on successive lines of defense towards Rome.
By Stephen Kirrage [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0/deed.en)], via Wikimedia Commons
In early 1944, the Allies reached the Gustav Line, which had the famous Benedictine abbey of Monte Cassino in its center. The terrain, mostly mountainous, forested and crossed by rivers, favored the defenders. It took no less than four months and a series of offensives initiated by contingents from various Allied nations, for the Allies to win the Battle of Monte Cassino.
At about the same time when the Battle of Monte Cassino began, the Allies landed at Anzio - located between Rome and the Gustav Line. The Germans managed to stop the Allied advance; then there was a standoff for several months. The Battle of Anzio would be won by the Allies only after the Germans began retreating, following the breakthrough of the Gustav Line in May 1944.
In August 1944, the Allies began the assault on the Gothic Line, which was the last great obstacle used by Wehrmacht to defend the northern Italy. Part of the Allied divisions had been transferred from Italy to France, and the Germans held out long enough so that the weather to become their ally. First, the autumn rains turning the ground into mud and making difficult the air support, and then the winter, contributed to a slow Allied advance, the Allies achieving partially their objectives .
In the spring of 1945, the Allies resumed their offensive, and the Italian Campaign would end with just a few days before the final victory in Europe.
Bundesarchiv, Bild 183-J16378 / Slickers / [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0/de/deed.en)], via Wikimedia Commons