Cutting structures for use with downhole tools in subterranean boreholes include a blade, a plurality of primary cutting elements coupled to the blade, and at least one secondary element rotationally leading the plurality of primary cutting elements in a direction of intended rotation of the cutting structure. The at least one secondary element is coupled to the blade proximate a leading surface of the blade and comprises at least one of a rubbing surface and a cutting surface. An exposure of at least one primary cutting element of the plurality of primary cutting elements is greater than an exposure of the at least one secondary element. Downhole tools such as reamers include cutting structures. Methods of enlarging a subterranean borehole include reaming a borehole with cutting structures.