Direct steam generation coupled with solar energy is a promising technology which can reduce the dependency on fossil fuels. It has the potential to impact the power-generation sector as well as industrial sectors where significant quantities of process steam are required. Compared to conventional concentrated solar power systems, which use synthetic oils or molten salts as the heat transfer fluid, direct steam generation offers an opportunity to achieve higher steam temperatures in the Rankine power cycle and to reduce parasitic losses, thereby enabling improved thermal efficiencies. However, this is associated with non-trivial challenges, which need to be addressed before such systems can become more economically competitive. Specifically, important thermal-energy processes take place during flow boiling, flow condensation and thermal-energy storage, which are highly complex, multi-scale and are multi-physics in nature that involve phase-change, unsteady and turbulent multiphase flows in the presence of conjugate heat transfer. This paper reviews our current understanding and ability to predict these processes, and knowledge that has been gained from experimental and computational efforts in the literature. In addition to Rankine cycles, organic Rankine cycle applications, which are relevant to lower operating temperature conditions, are also considered. This expands the focus to beyond water as the working fluid and includes refrigerants also. In general, significant progress has been achieved, yet there remain challenges in our capability to design and to operate effectively high-performance and low-cost systems with confidence. Of interest are the flow regimes, heat transfer coefficients and pressure drops during the thermal processes present in direct steam generation systems including those occurring in the solar collectors, condensers and relevant energy storage schemes during thermal charging and thermal discharging. A brief overview of some energy storage options are also presented to motivate the inclusion of thermal energy storage into direct steam generation systems.