The significant growth of the Si photovoltaic industry has been so far limited due to the high cost of the Si photovoltaic system. In this regard, the most expensive factors are the intrinsic cost of silicon material and the Si solar cell fabrication processes. Conventional Si solar cells have p-n junctions inside for an efficient extraction of light-generated charge carriers. However, the p-n junction is normally formed through very expensive processes requiring very high temperature (${sim}1000^{circ}C$). Therefore, several systems are currently under study to form heterojunctions at low temperatures. Among them, carbon nanotube (CNT)/Si hybrid solar cells are very promising, with power conversion efficiency up to 15%. In these cells, the p-type Si layer is replaced by a semitransparent CNT film deposited at room temperature on the n-doped Si wafer, thus giving rise to an overall reduction of the total Si thickness and to the fabrication of a device with cheaper methods at low temperatures. In particular, the CNT film coating the Si wafer acts as a conductive electrode for charge carrier collection and establishes a built-in voltage for separating photocarriers. Moreover, due to the CNT film optical semitransparency, most of the incoming light is absorbed in Si; thus the efficiency of the CNT/Si device is in principle comparable to that of a conventional Si one. In this paper an overview of several factors at the basis of this device operation and of the suggested improvements to its architecture is given. In addition, still open physical/technological issues are also addressed.