The recent increase in complexity of computations and the expansion of edge computing have led to the emergence of high power density data centers with an urgent demand for more advanced thermal management systems. Two-phase passive cooling systems such as thermosyphons and heat pipes have been widely used in industry to maintain the temperature of the servers below the threshold of failure and carry away a large quantity of heat from a small area. Such systems are economically viable and sustainable since they have no moving parts and consume lower power. However, an upgrade to these cooling systems is imminent due to the ever-increasing power densities of the data centers and more challenging thermal management issues faced by the industry. Nanofluids have emerged recently as a new class of cooling liquids claiming to enhance the heat transfer performance in single and two-phase cooling systems. As per several studies presented in this paper, the thermal performance of thermosyphons is shown to be enhanced by employing nanofluids. In this paper, a comprehensive review is presented on the effect of nanofluids in improving the Critical Heat Flux (CHF) and Heat Transfer Coefficient (HTC) in two-phase cooling systems. The boiling phenomenon and working principles of thermosyphons will be discussed to understand the underlying mechanisms affecting heat transfer in the evaporator region, where the heat is absorbed from the source. The impact of nanoparticle features, concentration, and deposition pattern on HTC enhancement will also be studied. Additionally, estimates of the heat dissipation improvement by using nanofluids along with the bottlenecks and challenges faced in applying such fluids practically are reviewed as well. In conclusion, recommendations are made for future research needed to overcome the risks and commercialize the nanofluids in two-phase cooling systems for providing significant improvement in heat transfer performance as compared to conventional working fluids.