Seismic hazard modelling is a multi-disciplinary science that aims to forecast earthquake occurrence and its resultant ground shaking. Such models consist of a probabilistic framework that quantifies uncertainty across a complex system; typically, this includes at least two model components developed from Earth science: seismic-source and ground-motion models. Although there is no scientific prescription for the forecast length, the most common probabilistic seismic hazard analyses consider forecasting windows of 30 to 50 years, which are typically an engineering demand for building code purposes. These types of analyses are the topic of this review paper. Although the core methods and assumptions of seismic hazard modelling have largely remained unchanged for more than 50 years, we review the most recent initiatives which face the difficult task of meeting both the increasingly sophisticated demands of society and keeping pace with advances in scientific understanding. A need for more accurate and spatially precise hazard forecasting must be balanced with increased quantification of uncertainty and new challenges such as moving from time-independent hazard to forecasts that are time-dependent and specific to the time-period of interest. Meeting these challenges requires the development of science-driven models which integrate all information available, the adoption of proper mathematical frameworks to quantify the different types of uncertainties in the hazard model, and the development of a proper testing phase of the model to quantify its consistency and skill. We review the state-of-the-art of the national seismic hazard modeling, and how the most innovative approaches try to address future challenges.