Catastrophe (CAT) risk models are commonly used in the (re)insurance industry and by public organizations to estimate potential losses due to natural hazards like earthquakes. Conventional earthquake risk modelling involves several significant modelling assumptions, which mainly neglect: (a) the interaction between adjacent faults; (b) the long-term elastic-rebound behaviour of faults; (c) the short-term hazard increase associated with aftershocks; and (d) the damage accumulation in building assets that results from the occurrence of multiple earthquakes in a short time window. Several recent earthquake events/sequences (e.g., 2010/2012 Canterbury earthquakes, New Zealand; 2019 Ridgecrest earthquakes, USA; 2023 Turkey-Syria earthquakes) have emphasised the simplicity of these assumptions and the need for earthquake risk models to start accounting for the short-and long-term time-dependent characteristics of earthquake risk. This thesis introduces an end-to-end framework for time-dependent earthquake risk modelling that incorporates (a) advancements in long-term time-dependent fault and aftershock modelling in the hazard component of the risk modelling framework; and (b) vulnerability models that account for the damage accumulation due to multiple ground motions occurring in a short period of time. The long-term time-dependent fault model used incorporates the elastic-rebound motivated methodologies of the latest Uniform California Earthquake Rupture Forecast (UCERF3) and explicitly accounts for fault-interaction triggering between major known faults. The Epidemic-Type Aftershock Sequence (ETAS) model is used to simulate aftershocks, representing the short-term hazard increase observed after large mainshocks. Damage-dependent fragility and vulnerability models are then used to account for damage accumulation. Sensitivity analyses of direct economic losses to these time dependencies are also conducted, providing valuable guidance on integrating time dependencies in earthquake risk modelling.