The give everyone an overview:
British sector (Second Army)
6th Airborne Division was delivered by parachute and glider to the east of the River Orne to protect the left flank.
1st Special Service Brigade comprising No.3, No.4, No.6 and No.45(RM) Commandos landed at Ouistreham in Queen Red sector (leftmost). No.4 Commando were augmented by 1 and 8 Troop (both French) of No.10 (Inter Allied) Commando.
I Corps, 3rd Infantry Division and the 27th Armoured Brigade on Sword Beach, from Ouistreham to Lion-sur-Mer.
No.41(RM) Commando (part of 4th Special Service Brigade) landed on the far right of Sword Beach.
Canadian 3rd Infantry Division, Canadian 2nd Armoured Brigade and No.48 (RM) Commando on Juno Beach, from Saint-Aubin-sur-Mer to La Rivière-Saint-Sauveur.
No.46(RM) Commando (part of 4th Special Service Brigade) at Juno to scale the cliffs on the left side of the Orne River estuary and destroy a battery. (Battery fire proved negligible so No.46 were kept off-shore as a floating reserve and landed on D+1).
XXX Corps, 50th (Northumbrian) Infantry Division and 8th Armoured Brigade on Gold Beach, from La Rivière to Arromanches.
No.47(RM) Commando (part of 4th Special Service Brigade) on the West flank of Gold beach.
79th Armoured Division operated specialist armour ("Hobart's Funnies") for mine-clearing, recovery and assault tasks. These were distributed around the Anglo-Canadian beaches.
U.S. Sector (First Army)
V Corps, 1st Infantry Division and 29th Infantry Division on Omaha Beach, from Sainte-Honorine-des-Pertes to Vierville-sur-Mer.
2nd and 5th Ranger Battalions at Pointe du Hoc (The 5th diverted to Omaha).
VII Corps, 4th Infantry Division and the 359th RCT of the 90th Infantry Division on Utah Beach, around Pouppeville and La Madeleine.
101st Airborne Division by parachute around Vierville to support Utah Beach landings.
82nd Airborne Division by parachute around Sainte-Mère-Église, protecting the right flank. They had originally been tasked with dropping further west, in the middle part of the Cotentin, allowing the sea-landing forces to their east easier access across the peninsula, and preventing the Germans from reinforcing the north part of the peninsula. The plans were later changed to move them much closer to the beachhead, as at the last minute the 91st Air Landing Division was found to be in the area.
British Airborne landings
East of the landing area, the open, flat, floodplain between the Orne and Dives Rivers was ideal for counter-attacks by German armour. However, the landing area and floodplain were separated by the Orne River, which flowed northeast from Caen into the Bay of the Seine. The only crossing of the Orne River north of Caen was 7 km from the coast, near Bénouville and Ranville. For the Germans, the crossing provided the only route for a flanking attack on the beaches from the east. For the Allies, the crossing also was vital for any attack on Caen from the east.
The tactical objectives of the British 6th Airborne Division were to capture intact the bridges of the Bénouville-Ranville crossing, to defend the crossing against the inevitable armoured counter-attacks, to destroy German artillery at the Merville battery, which threatened Sword Beach, and to destroy five bridges over the Dives River to further restrict movement of ground forces from the east.
Airborne troops, mostly paratroopers of the 3rd and 5th Parachute Brigades, began landing after midnight, June 6 and immediately encountered elements of the German 716th Infantry Division. At dawn, the Battle Group von Luck of the 21st Panzer Division counter-attacked from the south on both sides of the Orne River. By this time the paratroopers had established a defensive perimeter surrounding the bridgehead. Casualties were heavy on both sides but the airborne troops held. Shortly after noon, they were reinforced by commandos of the 1st Special Service Brigade. By the end of D-Day, 6th Airborne had accomplished each of its objectives. For several days, both British and German forces took heavy casualties as they struggled for positions around the Orne bridgehead. For example, the German 346th Infantry Division broke through the eastern edge of the defencive line on June 10. Finally, British paratroopers overwhelmed entrenched panzergrenadiers in the Battle of Bréville on June 12. The Germans did not seriously threaten the bridgehead again. 6th Airborne remained in the line until it was evacuated in early September.
American Airborne landings
The U.S. 82nd (Operation Detroit) and 101st Airborne Divisions (Operation Chicago) were less fortunate in quickly completing their main objectives. Partly owing to unmarked landing zones, radio silence, poor weather and difficult terrain, many units were widely scattered and unable to rally. Efforts of the early wave of pathfinder teams to mark the landing zones were largely ineffective. Some paratroopers drowned when they landed in the sea or in areas deliberately flooded by the Germans.
After 24 hours, only 2,500 of the 6,000 men in 101st had assembled. The dispersal of the American airborne troops, however, had the effect of confusing the Germans and fragmenting their response. In addition, the Germans' defensive flooding, in the early stages, also helped to protect the Americans' southern flank.
Many continued to roam and fight behind enemy lines for days. Most consolidated into small groups, rallied with NCOs or junior officers, and usually were a hodgepodge of men from different companies, battalions, regiments, or even divisions. The 82nd occupied the town of Sainte-Mère-Église early in the morning of June 6, giving it the claim of the first town liberated in the invasion. While some objectives were met (often with far fewer men than the mission planners intended), many paratroopers were too busy fighting for survival to take offensive action.
The campaign in Normandy is considered by historians to end either at midnight on 24/25 July 1944 (the start of Operation Cobra on the American front) or 25 August 1944 (the advance to the Seine). The original Overlord plan anticipated a ninety day campaign in Normandy with the ultimate goal of reaching the Seine; this goal was met with time to spare. The Americans were able to end the campaign on their front early with the massive breakout of Operation Cobra.
The US official history describes the fighting beginning on 25 July as the "Northern France" campaign, and includes the fighting to close the Falaise Gap, which the British/Canadians/Poles consider to be part of the Battle of Normandy.
SHAEF, back in England, and the governments were very nervous of stagnation, and there were reports of Eisenhower requesting Montgomery's replacement in July. Lack of forward progress is often attributed to the nature of the terrain in which much of the post-landing fighting in the US and parts of the British sectors took place, the bocage (small farm fields separated by high earth banks covered in dense shrubbery, well suited for defence), as well as the usual difficulties of opposed landings. However, as at El Alamein, Montgomery kept to his original attritional strategy, reaching the objectives within his original ninety day target.