An abrasive-impregnated cutting structure for use in drilling a subterranean formation is disclosed. The abrasive-impregnated cutting structure may comprise a plurality of abrasive particles dispersed within a substantially continuous matrix, wherein the abrasive-impregnated cutting structure exhibits an anisotropic wear resistance. One or more of the amount, average size, composition, properties, shape, quality, strength, and concentration of the abrasive particles may vary within the abrasive-impregnated cutting structure. Anisotropic wear resistance may relate to a selected direction, such as, for example, one or more of an expected direction of engagement of the abrasive-impregnated cutting structure with the subterranean formation and an anticipated wear direction. Anisotropic wear resistance of an abrasive-impregnated cutting structure may be configured for forming or retaining a formation-engaging leading edge thereof. A rotary drag bit including at least one abrasive-impregnated cutting structure is disclosed.