The development of new glassy materials is key for addressing major global challenges in energy, medicine, and advanced communications systems. For example, thin, flexible, and large-area glass substrates will play an enabling role in the development of flexible displays, roll-to-roll processing of solar cells, next-generation touch-screen devices, and encapsulation of organic semiconductors. The main drawback of glass and its limitation for these applications is its brittle fracture behavior, especially in the presence of surface flaws, which can significantly reduce the practical strength of a glass product. Hence, the design of new ultrastrong glassy materials and strengthening techniques is of crucial importance. The main issues regarding glass strength are discussed, with an emphasis on the underlying microscopic mechanisms that are responsible for mechanical properties. The relationship among elastic properties and fracture behavior is also addressed, focusing on both oxide and metallic glasses. From a theoretical perspective, atomistic modeling of mechanical properties of glassy materials is considered. The topological origin of these properties is also discussed, including its relation to structural and chemical heterogeneities. Finally, comments are given on several toughening strategies for increasing the damage resistance of glass products.