The ‘Big Muddy’ is described by Wikipedia as follows:
The Big Muddy Badlands are a series of badlands in southern Saskatchewan and northern Montana along Big Muddy Creek. They are found in the Big Muddy Valley, a cleft of erosion and sandstone along Big Muddy Creek. The valley is 55 kilometres (34 mi) long, 3.2 kilometres (2.0 mi) wide and 160 metres (520 ft) deep. The valley was formed when it was part of an ancient glacial meltwater channel that carried great quantities of water southeastward during the last ice age.
On the Saskatchewan side, guided tours are available out of Coronach. More information can be found here.
While we didn’t have time to take in any of the tours, Diane and I did manage to drive through the heart of the valley and see Castle Butte, pictured here:
The statistics of the butte are found on this sign:
As we were leaving, we noticed people on top of Castle Butte:
Here is a slideshow of the panoramic view in the valley: