Scratch-resistant glass substrates including a hard, scratch-resistant layer over a major surface of the substrate are disclosed. The layer may exhibit a hardness, as measured using a Berkovich indenter, of at least 10 GPa and an x-ray amorphous structure along at least a portion of the thickness of the layer. The layer may optionally exhibit an optical transparency of at least 70% and/or a compressive stress of at least 10 MPa.