By Stephen Mulvey
BBC News Online
By the end of D-Day the allies had gained a fragile foothold in Hitler's Europe.
They occupied four separate beachheads, at most a few miles deep, along a 30-mile section of the Normandy coast.
Just getting this far had cost an estimated 2,500 to 4,000 lives - but it was only the beginning.
For a while, the allies were at risk of being pushed back into the sea. They had to race to build up their invasion force faster than German commanders could move up reinforcements.
Sixty years later, historians still ask what would have happened if the bulk of the German 15th Army had arrived on the scene, instead of lying in wait for a second landing they had been led to expect in the Pas de Calais.
The allies won this race - despite the havoc caused by the worst June storm in the region for 40 years, and their lack of a major port - thanks to their domination of air and sea.
It was the subsequent task of pushing the German army out of Normandy, which caused real headaches, including some prolonged, bitter and bloody battles, often for small territorial gains.
The Land Forces commander for Operation Overlord, General Bernard Montgomery, had estimated that it would be possible to cross the Seine 90 days after D-Day.
In the event, the moment came 15 days early, on 20 August (D plus 75).
But the cost in human life was enormous. One in 10 of the two million allied soldiers deployed in Normandy had been lost - killed, wounded or missing.
British and Canadian units in Normandy had already lost more soldiers than there were left in reserves and even the US army was having difficulty keeping units up to strength.
Some US regiments had lost more than 100% of their complement of officers.
There had also been periods when the allies had seemed to be beating their heads against a brick wall.
Allied Supreme Commander General Dwight Eisenhower wrote in his memoirs: "Late June was a difficult time for all of us. More than one of our high-ranking visitors began to express the fear that we were stalemated and those who had prophesied a gloomy fate for Overlord were being proved correct."
The two main reasons for this were the strength of the Germany defence, and the difficulty of the terrain.
Military historian Robin Neillands writes in a recent book, The Battle of Normandy 1944, that "the outstanding army in Normandy" was the German army.
He adds: "In terms of kit, training, tactical ability, tenacity and sheer guts, fighting without air cover or naval gunfire support and hampered by interference from Adolf Hitler, the German army was undoubtedly the best in the field - and the feat of overcoming it should therefore not be underrated."
The German soldiers were also fighting a defensive battle in countryside ideal for defence.
Much of inland Normandy is, or was in 1944, bocage country, characterised by small fields, high hedgerows and sunken lanes.
Tanks were very vulnerable, and hamstrung by a host of natural tank traps. They had difficulty crossing the high banks along the field boundaries, on which the hedges grow, and often could not even turn their turrets in the lanes.
This placed a huge burden on the infantry.
Harvey Smith, of the Royal Engineers, writes on the BBC History People's War website: "Bocage country could be a nightmare, you could only see as far as the next field and in the lanes, only as far as the next bend.
"At night, German self-propelled guns stalked the hedgerows."
Many Normandy hedges have been pulled up, but sunken lanes remain
Trooper Leslie Dinning of the 1st Royal Tank Regiment makes the same point:
"In the Normandy bocage all the fighting, apart from that on the coast and around Caen, was by ambush. Obviously the attacking troops were at a disadvantage because they had to move forward.
"Poke their nose round corners where sitting a few yards up the road was a bloody big Tiger, Panther [German tanks] or a self-propelled gun, literally waiting for us and BANG! You had no chance."
Both the British/Canadian and US armies had to deal with this terrain - often without any preparation. Some units had fought in North Africa, others had done all their training in Salisbury Plain, Dartmoor or Norfolk.
According to one estimate, US forces lost 40,000 men during a 20-day advance on the strategic town of St Lo, which they finally took in mid-July - a cost of about one man per yard.
In many other Normandy battlegrounds too, losses were reminiscent of the worst World War I killing fields.
The allied advantage in sheer numbers of men and tanks was one reason for their success.
Montgomery's plan for Normandy was matched to the terrain: it called for the British and Canadian forces to tie down as many German units as possible near Caen, so that the defensive line would be stretched to breaking point further west.
This would allow the US forces to break a path to the south out of the bocage, then wheel round to the east.
This is eventually what happened. Once in open country, facing minimal resistance, the US Third Army was able to cover 50 or 60 miles per day.
In the first two weeks of August it cleared Brittany, swooped down to the Loire river, and passed through Le Mans before some units turned north, helping to encircle the German 7th Army near Falaise.
That encirclement led quickly to the end of the German army in Normandy and put the allies firmly on the road to Berlin.