I'll assume that you're only interested in Europe, and are uninterested in Soviet contributions (which were critical).
- A series of battles in North Africa that seesawed across the landscape. This theater was active from the Fall of France until Operation Torch (mentioned later)
- An ongoing battle in the Atlantic to keep supplies flowing to the UK.
- Sunk the Bismark
- Won the Battle of Britain
- Began daylight bombing by the British. When that was too costly the British moved to night bombing raids.
- Operation Torch in 1942 saw the US invade northern Africa in conjunction with a British offensive from the east.
- Operation Husky was the Allied invasion of Sicily in 1943.
- This was followed by the Allied invasion of Italy
- The US began daylight bombing in 1943 and learned for themselves that this was too costly without escorting fighters. Such daylight raids were again suspended until long range escorts could be introduced large numbers in 1944. The resulting war of attrition over Germany degraded the Luftwaffe to the point where it could not contest a cross channel invasion.
- Rome was liberated on June 4, 1944--mere days before D-Day.
Allied forces held on in northern Africa, stayed afloat (and refitted) until the US entered the war, then built up the invasion force that would land on D-Day. They also won the Battle of the Atlantic and secured aerial superiority so they could invade. Sicily and Italy were invaded as well. There was a ton going on from Dunkirk to D-Day.