Achieving high-efficiency solar cells and at the same time driving down the cell cost has been among the key objectives for photovoltaic researchers to attain a lower levelized cost of energy (LCOE). While the performance of silicon (Si) based solar cells have almost saturated at an efficiency of~25%, III-V compound semiconductor based solar cells have steadily shown performance improvement at~1% (absolute) increase per year, with a recent record efficiency of 44.7%. Integration of such high-efficiency III-V multijunction solar cells on significantly cheaper and large area Si substrate has recently attracted immense interest to address the future LCOE roadmaps by unifying the high-efficiency merits of III-V materials with low-cost and abundance of Si. This review article will discuss the current progress in the development of III-V multijunction solar cell integration onto Si substrate. The current state-of-the-art for III-Von-Si solar cells along with their theoretical performance projections is presented. Next, the key design criteria and the technical challenges associated with the integration of III-V multijunction solar cells on Si are reviewed. Different technological routes for integrating III-V solar cells on Si substrate through heteroepitaxial integration and via mechanical stacking approach are presented. The key merits and technical challenges for all of the till-date available technologies are summarized. Finally, the prospects, opportunities and future outlook toward further advancing the performance of III-V-on-Si multijunction solar cells are discussed. With the plummeting price of Si solar cells accompanied with the tremendous headroom available for improving the III-V solar cell efficiencies, the future prospects for successful integration of III-V solar cell technology onto Si substrate look very promising to unlock an era of next generation of high-efficiency and low-cost photovoltaics.