With the increase of installed capacity of photovoltaic power plants, short-term photovoltaic forecast is playing an important role in electricity planning and scheduling of power system. This paper reviews the recent progress on the research of short-term photovoltaic forecasts, and discusses the advantages and limitation of direct and indirect prediction methods respectively. The result shows that the accuracy of indirect prediction is better than that of direct prediction. Without the irradiance prediction modeling, the direct prediction is relatively simple, in which the widely-used hybrid forecast method is much more adaptive and fault-tolerant. In addition, the paper also concludes that weather change is a crucial factor that affects the accuracy of short-term photovoltaic forecasts, and proposes several solutions to reduce the impact of weather conditions on photovoltaic forecasts.