Beginning with Operation Shingle, the allies obtained a foothold in Italy while the Germans were determined to make the allies job a difficult one starting with the Gustav line.
Once the Normandy invasion was concluded it was a cacophony of multiple allied drives to silence the German offensives with having to deal with some strong defensive fronts and offensive attacks.
In 1943, Britain began bomber offensives over Germany's war production sites, some without fighter protection because of limited fuel capacity. Bombing targets and improved fighter protection would soon occur.
Adolf Hitler is desperate to stop the allies advance onto German soil and pushes a number of his military forces through the Ardennes and begins what has come to be known as the Battle of the Bulge. The allies had a number of clues that something was going to happen but ignored them.
A more detailed overview of the causes of the German assault through the Ardennes and the battle in Bastogne. The German line fell apart on the 25th after the weather cleared on the 23rd of December 1944. The allies then continued to drive toward the Rhine.