One of the most promising technologies for electricity supply is photovoltaic (PV) solar energy conversion that converts directly the solar irradiance into electricity. The current emphasis of such technology is toward manufacturing high efficiency devices whilst at the same time reducing the fabrication cost. Multi-junction solar cells have the advantage among all other solar cell technologies of holding the current world record for conversion efficiency i.e. 44.7% under 297x concentrated sunlight. The conventional multi-junction solar cells are based on extremely expensive substrate materials resulting in high manufacturing device cost. The replacement with crystalline silicon (c-Si) substrate, not only as a growth substrate, but also as the lowermost active sub-cell, leads to substantial cost reduction. This work presents a comprehensive calculation of the conversion efficiency limits of multi-junction solar cells based on Si substrate combined with theoretical and experimental studies of the required properties of the Si cell. Limiting conversion efficiencies above 43% and 48% for two- and three-junction tandem devices respectively are deduced for Si based solar cells under one sun AM1.5G spectrum. An important part besides the limiting efficiency potential is modelling the lowermost Si solar cell itself including different Si solar cell structures i.e. Passivated Emitter Rear Locally diffused (PERL), Passivated Emitter Rear Totally diffused (PERT) and rear emitter PERT. Indeed, the optimization conditions are substantially different when using the Si junction in a tandem structure compared with illumination of a single junction Si cell under the full solar spectrum. In particular, the design of the upper junctions on the Si substrate is crucial. Even with the presence of a buffer layer between the gallium arsenide (GaAs) and Si substrate, inevitable threading dislocations degrade the performance of a GaAs top junction. Thus, the design of a top junction GaAs cell on Si substrate differs from the typical single-junction GaAs thin film structure. Similarly, the recent emergence of organic-inorganic halide perovskite as a candidate top junction on c-Si has been investigated suggesting a tandem conversion efficiency close to 30% with presently demonstrated material and device properties. Additionally, the impact of a germanium (Ge) buffer layer on the Si sub-cell performance is studied. The buffer layer aims to accommodate the lattice mismatch between III-V materials and the Si substrate. Further, having the Ge layer thick enough and of sufficient crystal quality to be used as an active cell in a novel “out-of-sequence tandem architecture” is investigated.