Drilling tools, such as drill bits, having a shank, a crown, and a plurality of abrasive cutting elements. In the case of impregnated drilling tools, the abrasive cutting elements are dispersed throughout at least a portion of the crown. In the case of surface-set drilling tools, the abrasive cutting media is secured to and projects from a cutting face of the crown. The matrix of the crown of the drilling tools includes a carbide-forming alloy that forms a direct carbide bond with at least one cutting element of the plurality of abrasive cutting elements.