In order to lessen reliance on fossil fuels, a rise in interest in the utilization of fluctuating and intermittent heat sources derived from renewable energy (such as solar thermal, ocean thermal, and geothermal) and waste heat has been observed. These heat sources could be used to generate electricity at relatively low and medium temperatures, for example, through the organic Rankine cycle (ORC). In some case studies, various approaches have been developed to deal with and design ORCs in the desired operating condition utilizing suitable working fluids. This article aims to review some designs and integrated systems of ORC with thermal energy storage (TES) and a two-phase expansion system focusing on the utilization of medium- and low-temperature heat sources in which some subcritical ORCs are presented. Moreover, several possible control systems (both conventional and advanced ones) of ORC with TES and a two-phase expansion system are reported and compared. At the end of this article, the possible future developments of design and control systems are discussed to describe advanced ORC for utilizing low-grade heat sources. This study aims to provide researchers and engineers with an insight into the challenges involved in this process, making industrialization of ORC technology more extensive, in particular when combined with TES and a two-phase expansion system.