Dynamics of lithospheric plates resulting in localisation of tectonic stresses and their release in large earthquakes provides important information for seismic hazard assessments. Numerical modelling of the dynamics and earthquake simulations have been changing our view about occurrences of large earthquakes in a system of major regional faults and about the recurrence time of the earthquakes. Here, we overview quantitative models of tectonic stress generation and stress transfer, models of dynamic systems reproducing basic features of seismicity, and fault dynamics models. Then, we review the thirty-year efforts in the modelling of lithospheric block-and-fault dynamics, which allowed us to better understand how the blocks react to the plate motion, how stresses are localised and released in earthquakes, how rheological properties of fault zones exert influence on the earthquake dynamics, where large seismic events occur, and what is the recurrence time of these events. A few key factors influencing the earthquake sequences, clustering, and magnitude are identified including lithospheric plate driving forces, the geometry of fault zones, and their physical properties. We illustrate the effects of the key factors by analysing the block-and-fault dynamics models applied to several earthquake-prone regions, such as Carpathians, Caucasus, Tibet-Himalaya, and the Sunda arc, as well as to the global tectonic plate dynamics.