Methods for machining glass structures may be performed on fusion-drawn glass laminates having a core layer interposed between a first cladding layer and a second cladding layer. The core layer may be formed from a core glass composition having a core photosensitivity, the first cladding layer may be formed from a glass composition having a photosensitivity different from the core photosensitivity, and the second cladding layer may be formed from a glass composition having a photosensitivity different from the core photosensitivity. At least one of the core layer, the first cladding layer, and the second cladding layer is a photomachinable layer. The methods may include exposing a selected region of a photomachinable layer in the fusion-drawn laminate to ultraviolet radiation; heating the glass structure until the selected region crystallizes; and removing the crystallized material selectively from the photomachinable layer.