Geologically Galdhøpiggen, as most of Southern Norway's mountain ranges, belongs to the Caledonian folding. The peak is made of gabbro, a hard but rather coarse-grained rock which is found in most of the Jotunheimen range. During the ice ages it was heavily glaciated and got its present form. The theory that the highest summits in Norway stayed above the ice as nunataks has been abandoned by most geologists. It fits well with the present flora in the area, but it does not fit well with the present knowledge of ice thickness and the results of glaciation.
For many years, Norwegians did not know that Galdhøpiggen was their highest summit. The honor was granted to the much more visible Snøhetta in the Dovrefjell range. Hence no attempts were made to climb the peak, while Snøhetta was visited for the first time in 1798 as part of a scientific trip to the area. In 1844 the geologist and mountaineer, Baltazar Mathias Keilhau, made two unsuccessful attempts to reach the summit. On one of these he reached the summit which later was named Keilhaus topp 2,355 m above sea level very close to Galdhøpiggen, but the terrible weather forced them to return.
In 1850 three men from Lom reached the summit, the guide Steinar Sulheim, the local teacher Arnesen and the church warden Flotten.
Access to the top of Galdhøpiggen is not especially hard: four hours walk up, two hours down; from Juvasshytta (1850 metres above sea level) it takes about three hours up (including about 45 minute to prepare for crossing the Styggebreen glacier) glacier, an hour at the top and about two hours back.
Galdhøpiggen can also be hiked from the Spiterstulen lodge in Visdalen, with a technically very easy, but still somewhat strenuous climb of 1300 m — nearly 4000 ft. From Spiterstulen, hikers do not have to cross the Styggebreen glacier, and hence a guide is not required. Ardent peak-baggers may count three summits on the route from Spiterstulen, Svellnose, Keilhaus topp and the summit itself.
Galdhøpiggen had earlier been challenged for the title as the highest mountain in Norway by Glittertind, as some measurements showed Glittertind was slightly higher including the glacier at its peak. That glacier has, however, shrunk in recent years, and Glittertind is now only 2464 m even including the glacier. Hence, the dispute has been settled in Galdhøpiggen's favour.
At the summit a small cabin has been built. In the summer soft drinks, chocolate bars, postcards and other items are sold here. Earlier the Norwegian Postal Authority had a small post office here—being the highest in Northern Europe.
A sign which states that inline skates are strictly forbidden inside the cabin may be a somewhat superfluous warning, since heavy boots are the footwear up there.
Galdhøpiggen is not only the highest summit in Northern Europe. It also contains two probably unbreakable horticultural records in Northern Europe, being the upper limit for Ranunculus glacialis (2370 m) and Saxifraga oppositifolia (2350 m). Since the summer might not occur at all, some years, it tells something about these flowers' adaptation to the extremely harsh climate.
On sunny days in the later part of July and August, the summit is visited by hundreds of people.