If the Caucasus is not held to be "European", then Mont Blanc is the highest point in Europe. Arguments rage back and forth over whether Mont Blanc or Elbrus in far southern Russia deserves this title, but, given a strict definition of the Asia-Europe boundary as the crest of the Caucasus, Elbrus is the king and therefore one of the famous "Seven Summits".
Blanc, however, has more isolation (distance to a higher peak) than Elbrus, and it is clearly the dominant summit of the large western peninsula of the Eurasian landmass. By any measure the monarch of the Alps is one of the world's premier summits.
A massive dome of snow, Blanc is one of the many instances in the world of the highest point in a range being one of the easier major summits to climb. The sheer size of Mont Blanc makes its summit area a broad, gentle crest, and routes from the French side are generally easier than the massive, jumbled face rising from the Italian half of the mountain.
French maps show the France-Italy border following the watershed line in the Mont Blanc Massif, except for a curious jog to the south that fully encloses the immediate summit area of Mont Blanc as totally in France. Italian maps show the boundary following the watershed line in full, with the summit on the border of the two nations. This is curious state of affairs, and it is not 100% clear which country is sovereign in a small patch of snow at the very apex of the Alps.
This web site takes the Italian view, and lists Mont Blanc as the highest point in both France and Italy. The reasons are: huge precedent for boundaries following watersheds around the world; nothing significant is lost to France by sharing the peak, while the Italians gain a real national high point; and no historic document or treaty can be found to support the unusual jog in the border.
The standard and easiest route begins at the end of the Mont Blanc Tramway, a cog railway leading from Le Fayet and St. Gervais-les-Bains up to Nid d'Aigle at 2372m. From there a hiking path leads to the vicinity of the Tete Rousse hut at 3167m, and then the route reaches the most difficult section, the long ascent of the crumbling rock of the steep northwest face of the Aiguille du Gouter. Steel cables make technical rock-climbing gear
unecessary, but rockfall down a gully that has to be crossed can be dangerous.
At the top of this steep face lies the Gouter hut at 3817m, and from there the route follows a long, snowy, undulating ridgecrest over several minor bumps, the net effect always up, to the summit. Crevasses are rarely present on this ridge walk, and if the weather is good the only problems are the incredible crowds of climbers and the increasingly thin air. A careful and confident climber should have no trouble soloing this peak.
It's best to hike to the Gouter Hut the first day, and then get an early start the next morning for the summit. On my climb I stayed at the lower Tete Rousse hut, figuring it would be less crowded, but I had to start up at 1 AM and face the crumbling rock face in the pitch blackness. Like most huts in the Alps, both the Tete Rousse and Gouter huts can get very crowded, noisy, and unsanitary. Some people bivouac outside near the huts and get away with it, despite the technical illegality of the practice.
There are other routes on Mont Blanc, of course. A long climb can be made directly from Chamonix via the Grand Mulets hut, but the larger vertical gain and nasty crevasse problems make this route much more serious than the Gouter route. Intrepid climbers also start at the top of the Aiguille du Midi cable car and climb Mont Blanc de Tacul and Mont Maudit on the way to Mont Blanc in one very long day.