Wear sensors are provided on a drill bit or other rotary cutting tool which is for operation in a subterranean borehole and has a plurality of separate cutters protruding from a support structure towards the material to be cut by the tool. The electrically operated sensing means are located at or coupled to a sensing point within a protrusion from the support structure. This sensing point is located within a protrusion such that attrition of at least one cutter to a partially worn state brings the protrusion into abrasive contact with the material being cut and attrition of the protrusion then exposes the sensing point to the material which is being cut by the tool and thereby brings about a detectable change, which may include damage to the sensor at the sensing point, indicative of wear. The tool includes means to communicate data from the sensing means to the surface.