In recent years, the parameter extraction methods of solar cell have attracted a lot of research attention. The reason is that the matching solar cell parameters can effectively reduce the influences of internal and external factors on photovoltaic efficiencies. In this paper, the five-parameter extraction methods of solar cell single-diode model are discussed in detail. The five parameters are the photocurrent, the reverse diode saturation current, the ideality factor of diode, the series resistance, and the shunt resistance. In fact, the existing research methods are classified as four categories, namely, analytically extracting parameter methods, extracting parameter methods with the help of Lambert W function, constructing or using special functions to extract parameter methods, and using intelligent algorithm to extract parameter methods. In this article, we not only elaborate their main theories and approaches, but also discuss their advantages and disadvantages. The main conclusion is that the analytical method for the extraction of solar cell model parameters requires some assumptions. Therefore, this method is fast but less accurate due to various approximations. In addition, the parameter extraction using the analytical method needs a thorough calculation, and deducing the actual values of (dI/dV)|V=Voc and (dI/dV)|I=Isc and peak power point is also challenging. When the five parameters of solar cell are calculated using the Lambert W-function method, the results show that the extraction process is easier when using the consecrated software such as MATLAB, but the larger computational time is needed. Generally, the Lambert-W function provides the exact explicit expression for parameter extraction. As a result, the accuracy of approximate solution using Lambert-W function is much higher than that of the above method. It is obvious that the accuracy of using special functions to extract cell parameters is limited by those function characteristics. Of course, those special functions, such as Green's function, seem to be complex approaches. The accuracy of the extracting cell parameters by using intelligent algorithm strongly depends on the type of fitting algorithm, the fitting criterion, objective function and the starting values of the parameters. Finally, based on the conducted review, the future research trend of parameter extraction is also predicted