Atomic arrangements systemically deviating from the classic definition of single crystal lattice have been known in spherulites for over a century. However, their unusual curved lattice could not be exploited for useful applications due to their uncontrolled orientations and lattice curvatures. Heating of glass with focused laser, electron, or X-ray beam has yielded well-defined conditions for forming single crystal architectures. Furthermore, by controlling the conditions of irradiation and confinement by glass matrix for a given system, desired lattice curvature (rotations and twists) can be reproducibly introduced into these crystals. Here, we review several examples of laser-fabricated crystals with curved lattices in glass using a common coordinate system, which helps to establish correlations between processing parameters and lattice curvature. The mechanisms of lattice deformations are discussed along with potential methods to control the orientation of the initially formed seeds that determine the lattice orientations of the end product. The recent developments of laser-fabrication of single crystal architectures in glass with controlled heating profile appear promising for engineering the curvature of their lattices.