Direct steam generation (DSG) in parabolic-trough collectors (PTC) is one of the most attractive technologies in concentrated solar power plants. Its appeal stems from its ability to reduce the operational and maintenance costs compared with other heat transfer fluids. Modelling and simulation (M&S) tools, together with the development of experimental real-scale set-ups have played a key role in the advancement of this solar technology. The aim of this review is to summarize and analyse the thermohydraulic, thermal and optical models implemented in M&S tools for DSG in PTC in order to identify the contribution that these models could provide towards the improvement of the technology in the future. Thermohydraulic models have been, in most cases, developed under the three-equation homogeneous equilibrium model (HEM) approach, successfully for recirculation mode. The more complete six-equation two-fluid model (TFM) approach, has also been properly applied, to a lesser extent, to modelling the once-through solar field operation mode, considering water/steam two-phase flow patterns. Although these advancements have contributed to the design and operation of the first commercial solar steam power plant with PTC for electricity generation, there are however some technological gaps still to be overcome to consolidate the technology. In recirculation solar field operation mode, the use of HEM has shown to be adequate to model the DSG process in PTC integrated with thermal energy storage systems and into solar hybrid power plants. For once-through operation mode, the distributed-parameter thermohydraulic models, especially under TFM approach, involving a detailed flow pattern map, have demonstrated to be suitable tools for solving the uncertainties related to the two-phase flow, especially at the endpoint of the evaporation section. •Technological advances of direct steam generation in parabolic-trough collectors together with current challenges are hereby described.•Thermohydraulic modelling approaches and the mathematical models implemented in modelling and simulation tools for direct steam generation in parabolic-trough collectors are discussed in detail.•Thermal and optical modelling approaches in the receiver tube of parabolic-trough collectors, as well as the ones applied for direct steam generation, are examined.•The potential contribution of modelling and simulation tools towards the improvement of the technology is identified both in recirculation and once-through operation modes.