Using ice axe tools on rock has been happening since mountaineering began, but the sport of “dry-tooling” as a climbing sport of its own is more of a modern discipline.
The movements are rather gymnastic and the technique is most often done to help train ice climbers during the shoulder season. Dry-tooling outdoors typically takes place in caves and overhanging rock surfaces that aren’t great for rock climbing. The routes are generally 50-percent natural holds and 50-percent man-made holds, which are drilled holes that climbers use to place the pick of their axes into. Indoor routes normally consist of plastic holds (think gym holds) that are drilled out for tools and have man-made holds which are scarred divots that climbers use to place the pick of their axes into.
It can be a bit awkward, but certainly a great way for climbers to train.