Accurately predicting the power produced during solar power generation can greatly reduce the impact of the randomness and volatility of power generation on the stability of the power grid system, which is beneficial for its balanced operation and optimized dispatch and reduces operating costs. Solar PV power generation depends on the weather conditions, such as temperature, relative humidity, rainfall (precipitation), global solar radiation, wind speed, etc., and it is prone to large fluctuations under different weather conditions. Its power generation is characterized by randomness, volatility, and intermittency. Recently, the demand for further investigation into the uncertainty of short-term solar PV power generation prediction and its effective use in many applications in renewable energy sources has increased. In order to improve the predictive accuracy of the output power of solar PV power generation and develop a precise predictive model, the authors used predictive algorithms for the output power of a solar PV power generation system. Moreover, since short-term solar PV power forecasting is an important aspect of optimizing the operation and control of renewable energy systems and electricity markets, this review focuses on the predictive models of solar PV power generation, which can be verified in the daily planning and operation of a smart grid system. In addition, the predictive methods identified in the reviewed literature are classified according to the input data source, and the case studies and examples proposed are analyzed in detail. The contributions, advantages, and disadvantages of the predictive probabilistic methods are compared. Finally, future studies on short-term solar PV power forecasting are proposed.