Full frame fisheye lenses with non-rectilinear optics designed for making very wide angle images of around 180 degrees across the diagonal and are typically used in such things as interior, landscape, wide field astronomical, rad x-sports and creative portraiture photography. Oh and just for old fashioned fun.
Non-rectilinear? Simply put they have loads of uncorrected barrel distortion which produces a curvilinear image where the centre of the image bulges outwards (especially noticeable close up) and straight lines curve madly (especially noticeable with straight lines from the edges of the frame curving inwards into the frame).
Use the lens on distant subjects without straight lines in them and keep it straight and parallel with the horizon and the curvilinear effects will pass almost unnoticed - landscapes can be a good subject for this - or keep the the subjects with straight lines broken up with detail like branches and foliage for example and curvature is much less noticed. Witness the bare tree trunks whose curvature really stands out compared to the others.
Similarly, point lens vertically and keep it straight with this axis and again the curvilinear effects are less noticeable like with tree canopy picture as below.
Give things a bit of weird curvilinear view by getting close up and using the barrel distortion combined with tremendous depth of focus to give you a new perspective on life, as below.
Finally, with such a wide view it easy to end up with bits of yourself or your gear in the picture unintentionally and unnoticed the photo so watch out.
In conclusion, full frame fisheye lenses are great fun to use and to experiment with but don't get too carried away as the images they produce can become quickly clichéd. But don't be discouraged they have their place and are a useful tool for many photogs who use them to great effect. More sample images here and also here.