Sólheimajökull is an outlet glacier of Mýrdalsjökull, the ice cap that sits above the Katla volcano, and it is one of the most accessible glaciers in Iceland for guided walking. The snout of the glacier is about 30 minutes' walk from the car park on a well-maintained path, and tours operating from Skógar and the Ring Road can take you onto the ice with crampons and ice axes within a couple of hours of arrival.
The glacier has retreated dramatically over the past century — the bare rock and scoured moraine you walk across on the approach were under ice within living memory — and that retreat is visible and measurable in a way that makes it one of the more concrete illustrations of climate change available to the visitor. The tour operators on the glacier are informative on this. The ice itself, when you're on it, is spectacular: blue and grey crevasses, meltwater pools, and rock debris from the volcano mixed into the surface. Tours are available from nearby operators and must be booked in advance in peak season.