The conversion efficiencies of perovskite solar cells based on organic-inorganic hybrid metal halide materials have broken through 22% in just a few years, which provides a ray of hope in solving the future energy problem, and receives great attention and research enthusiasm from the academic circle. However, what is followed is commercialization and industrialization process, which will greatly enhance the importance and urgency of the research and development of the green, non-toxic, highly-efficient, and lead-free perovskite solar cells. In order to speed up the development of these environment-friendly perovskite solar cells, we summarize the recent research progress in the perovskite solar cells from the two categories of Pb-free and less-Pb materials. In the Pb-free aspect Sn-based perovskite solar cells are emphatically introduced. A maximum efficiency of 8.12% is obtained for the solar cells based on FA0.75MA0.25SnI3, but it lags far behind the Pb-based competitors. This may be caused mainly by the oxidation of Sn2+ ions and the band mismatch with carrier transport materials, etc. So, for further improving the efficiency, it is very important to optimize the device structure and material properties, and understand the role played by Sn4+ ions in films. In addition, more attention should be paid to the inorganic halide double perovskite materials as potential solutions for the toxicity and stability issues. In the less-Pb part, Sn-doping contributes to a large reduction of lead content in the film, and a maximum efficiency of 17.6% for the (FASnI3)0.6(MAPbI3)0.4 perovskite solar cells is achieved with good long-term stability. What is even more interesting is that it can be utilized to construct tandem cells through the bandgap regulation after doping. However, it is very difficult to determine the optimum Sn-doping ratio. More systematic, rigorous and normative experiments are extremely necessary to reveal the interaction mechanism between Pb2+ and Sn2+. For other doped elements, the effects of their concentrations on the properties of thin films and the performance of solar cells are also emphatically discussed, and it is very urgent to have a further understanding of the working principles of devices and the fundamental functions of substitution elements. Thus, this review highlights the recent research efforts in the development of Pb-free and less-Pb perovskite solar cells and also provides a perspective of future development of new environment-friendly and high performance perovskite solar cells.