So the entirety of the British expeditionary force, the French First army and the Belgian army were all trapped by the "Manstein plan" which was devised by German general Erich Von Manstein while he was still an assistant to other German general Gerd Von Runstedt. Basically the allied armies were lured into advancing into Belgium (as was their pre-war plan for defeating Germany) and the German armour cut across the Ardennes forest, reaching the English channel and cutting them off in a big pocket. See this image The British and French tried several attempts to smash the German spearheads and later to break out of the pocket but lack of supplies for the allied divisions as well stout German defence, along with German air superiority ensured that the pocket remained intact. The British at once began to pull back towards Dunkirk, knowing that was their way out of France and that the battle at this point had been lost. Their hopes were further dashed when the Belgians capitulated leaving only the British and French first army in the pocket.

On May 26th, the British approved operation Dynamo where a large fleet of British ships began to stream towards Dunkirk. There was a problem where the British commander, Lord Gort, promised to leave some three British divisions to fight for the French but the government secretly told him to withdraw all British units from France. This angered the French, but none the less they still formed the rearguard to defend against the Germans while the British escaped. By June 2nd all British troops had been evacuated, but thankfully for the French, British naval and air support allowed some 50,000 extra French soldiers to escape before the German reached Dunkirk on June 4th. In the end, over 300,000 soldiers had been evacuated, 200,000 British and an extra 100,000 allied/French soldiers. Considering that while all this was going on, the allied positions were under constant air bombardment, makes the whole operation quite impressive, even though large amounts of equipment and French soldiers were left to be captured by the Germans.

Probably the most famous aspect of the battle is Hitler's famous "stop order" that he issued to parts of his army. Hitler later claimed that he let the British escape as a gesture of good will, that was really just an attempt by Hitler to save face. The truth is that Hitler's armoured divisions needed a serious resupply as they had been going nonstop since the invasion, and furthermore Goering had convinced Hitler that his Luftwaffe could finish the British off before they could escape. This would not be the last time Goering would mislead Hitler, famously claiming that he could supply all the troops in Stalingrad by air, convincing Hitler to not let them break out.