In reply to echo34:
As others have said, Iceland isn't really an (alpine) climbing venue – at least, not in the sense that it'd be a prime choice to compare with, say, the Alps.
But as others have also said, there is climbing to be done – though whether it'd be worth a trip for the cragging alone is, in my view doubtful: there are far better and, more committing and gnarlier things to do in the country. But I suppose it could be worth packing rock shoes for some bouldering, if the weather is good enough.
The alpine climbing prospects are genuine but the glaciers are either pretty easy or they are dangerous. I don't think there's much in between, as there is in the alps. Also, it could be tricky finding a suitable combination of season and good weather window, though Doug Scott did some difficult exploratory routes on Vatnajökull. There is quite a useful guide to walking/mountaineering in Iceland, including a few alpine routes up to ca. PD/AD. See Ari Trausti Guðmundsson, Summit: 100 Mountain Hikes in Iceland (Uppheimar, 2012). Some of the best routes are remote and inaccessible.
Scrambling? The rock is generally far too unreliable. What looks like Gritstone is Palagonite, which has about as much in common with grit as chalk.