Understanding the fracture toughness of glasses is a fundamental problem of prime theoretical and practical importance. In this work, its dependence on the loading rate, the age (history) of the glass and the notch radius is discussed. We show that the notch fracture toughness results from a competition between the initial plastic relaxation timescale, which depends on glass age and its preparation protocol, and an effective loading timescale, which depends on the notch radius, the system`s geometry and the external loading rate. The initial glass structure, which controls the initial plastic relaxation timescale, is characterized by a non-equilibrium temperature. The theory predicts a rather abrupt increase in the toughness – a brittle-to-ductile-like transition – as a function of the ratio between these two timescales. Novel experiments on Bulk Metallic Glasses (BMGs), which allow to carefully control the initial structural state of the glass and accurately measure the toughness, strongly support the theoretical predictions. In particular, they show that BMGs – can be significantly toughened by carefully controlling their initial state. These results highlight the importance of timescales competition and far from steady-state plastic deformation dynamics for understanding the toughness of glasses, and open up the way for a much broader usage of BMGs as tough, highly-reproducible structural materials.