Western Front of World War 2 saw two periods of intense battles: first in 1940, when Nazi Germany conquered much of Western Europe, and then in 1944-1945 when the Allies liberated the occupied countries and defeated for good the Third Reich.
In April 1940, Germany made the first move in the West by invading Norway and Denmark. Next month, Germany invaded the Low Countries and France, attacking with most of its armored divisions through the hilly and forested region of the Ardennes. After the breakthrough at Sedan, the Wehrmacht made the winning move in the Battle of France when the panzer divisions headed towards the English Channel.
Bundesarchiv, Bild 101I-055-1570-06A / Weber, Robert / [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0/de/deed.en)], via Wikimedia Commons
Then the Germans planned to invade Britain, but this required the Luftwaffe to achieve air superiority over the British Royal Air Force. Although excellent for tactical support, the German Air Force was not designed for strategic bombing. This drawback, as well as the fickle German strategy, led to a British victory in the Battle of Britain.
The next few years, there were no major battles on the Western Front.
The lull was interrupted on June 6, 1944 - D-Day - when the Western Allies landed in Normandy, northwestern France. The Allies managed barely after two months crucial breakthroughs, but they won the Battle of Normandy after the counterattack of the panzer divisions ended for the Germans in the disaster of Falaise.
In late September 1944, the Anglo-American Allies launched Operation Market Garden in the Netherlands, only partially successful, as the Allied airborne troops, awaiting for the British armor, tried to occupy and defend a series of bridges, but the last bridge, at Arnhem, remained in German hands.
During the same period, the Americans entered into Germany from the Belgian border, getting stuck for a few months in the bloody Battle of Hürtgen Forest.
In mid-December 1944, the Germans launched a stormy offensive through the Ardennes, code-named Operation Wacht am Rhein, aiming to reach the Belgian port of Antwerp. Helped by the bad weather which not allowed Allied air support, the Germans made a huge bulge in the front during the first week, hence the name of Battle of the Bulge.
After the weather has improved and the Patton's Third Army counterattacked, the Allies recovered all the lost ground by the end of January 1945. The Wehrmacht had lost the last significant forces that could stop the Allied advance into the heart of Germany.
The last major act occurred in early April 1945, when the U.S. 1st and 9th Armies met east of Rhine, trapping over 300,000 German soldiers in the Ruhr pocket. On May 7, Germany surrendered.