Electrically Driven Heat Pumps (EDHPs) have been identified as a key technology to reduce the energy consumption in the domestic space heating sector. However, since EDHPs require electrical power, they face issues related to network overload at peak-time, high operating costs, and increased carbon footprint. A promising alternative to address these shortcomings is the use of Thermally Driven Heat Pumps (TDHPs), which are powered by a heat source instead of electricity. TDHPs offer the possibility of running with numerous types of heat sources, even renewable ones. A promising TDHP technology is the ORC driven Heat Pump (HP-ORC). It consists in the combination of an Organic Rankine Cycle (ORC) and a Heat Pump (HP). This technology provides high flexibility in the heat source selection while offering the possibility of producing electricity. Furthermore, when combined with gas bearing supported turbomachinery, the HP-ORC technology offers an oil-free heating solution. The goal of this thesis is to identify the potential and challenges of the HP-ORC technology. Since HP-ORCs are complex systems, an integrated design and optimization procedure has been applied, aiming at objectives of performance, investment cost, and feasibility. While such integrated design procedures are attractive, they are complex and time consuming. Accurate reduced order models for the various system components are, therefore, highly beneficial for improving the design process. These models are, however, currently missing for small-scale turbomachinery, and hence are developed in a first step. These pre-design models are three orders of magnitude faster than mean-line analysis models while predicting isentropic efficiencies within a 4% error band. Moreover, the presented models provide updated design guidelines for radial turbomachinery and offer insights into the underlying phenomena that shape the efficiency contours. In a second step, the improved turbomachinery models have been used for the integrated optimization of the Compressor Turbine Unit (CTU). The results suggest that the performance trade-off is governed by the turbomachinery components. Further, the design robustness of the CTU is investigated, showing the importance of mitigating bearing manufacturing errors while having fluid leakage and turbomachinery tip clearances as small as possible. In a third step, the thermo-economic optimization of the HP-ORC is developed. For domestic heat pump applications, the optimum working fluid and heat exchanger design are retrieved. Using a hot source at 180°C, exergetic efficiencies over 50% and COPs above 1.8 are achieved, showing a 30% increase compared to the proof of concept. In addition, two configurations are compared, whether the ORC expander and HP compressor are mechanically coupled or not. Although the uncoupled HP-ORC offers more flexibility, it presents inferior thermo-economic trade-offs compared to the coupled configuration. The HP-ORC is compared to typical absorption systems, suggesting that single effect absorption heat pumps are competitive at low heat source temperatures (<120°C), whereas HP-ORCs outperform when the heat source temperature increases above 150°C. In a final step, the optimization tools developed in this thesis are applied to three case studies in which the HP-ORC may deploy its potential: domestic heating, greenhouse, and air conditioning in helicopters using the engine exhaust heat.