The invention provides a bit breaker comprising a plate that bounds a pipe slot. The bit breaker has two jaws that define two working surfaces located on opposite sides of the pipe slot. The two jaws are configured to move relative to the plate. In some embodiments, the invention is an assembly that further includes a pipe, tool section, tool or pipe joint received in the pipe slot. The pipe, tool section, tool or pipe joint has formed therein two crosswise grooves located on opposite sides of the pipe, tool section, tool or pipe joint. In some embodiments, the plate defines two fixed arms and a fixed base leg, with the two jaws mounted respectively against the two fixed arms. The bit breaker can have an adjustable arm such that the pipe slot can be surrounded about 360 degrees by the bit breaker.