The history of Great Danes is not a one version story. Some would argue the breed evolved primarily in Britain over several hundred years, while others would say the Germans did all of the work. So the history of Great Danes depends on which version you listen to!
Great Dane dog history first appears about 3000BC. We see Dane like dogs in carvings on Egyptian monuments built around this time. Fast forward 3400 years to the 5th century, when present day Europe was invaded by the Alanis, an Asiatic race, who brought giant mastiff dogs with them. Over the next several hundred years, it is surmized that these mastiff like dogs were cross bred with Irish Grey Hounds, producing a giant but slimmer breed than pure mastiff.
It is also possible that these large mastiff dogs were brought to Europe by the Romans. Over several hundred years the Celts cross bred these giants with either grey hound or Irish wolf hound (or perhaps both). This effort led to the development of the "English Dogge", which some would say is the ancestor to the Modern Great Dane.
It is probably true that both versions of Great Dane history are accurate and contributed to the beautiful animals we now enjoy, but certainly, the Germans deserve most of the credit for the development of the breed as we know it today. By the 16th century, these giant dogs were fairly common as boar hounds in both Britain and the Germanic states. The Germans did import a large number of these "Englishe dogges" for cross breeding with their own version as they worked to develop the perfect boar hunter for their own needs.
But here the history of the great dane takes another twist. Boar hounds were not cudly stoic dogs. European wild boar were very dangerous and hunting them required a fast, strong and aggressive dog. And that's what had been developed. But it was also realized, that a dog of this size could be an excellent guard dog - although in order to fulfill this function somthing would have to be done to make it more people friendly. And so over the 18th and 19th centuries, German dog breeders concentrated on evolving their boar hound into a breed of good temperment and friendliness.