In most of the countries around the world, solar photovoltaic power plants have a cost-competitive structure for providing energy access and for increasing electricity production. However, solar photovoltaic power integration requires the handling of power quality and stability problems due to its non-controllable and intermittent characteristics. At this point, the need for reliable solar irradiance and solar power forecasting is emerged for the optimal modeling and scheduling of solar photovoltaic power plants. For this purpose, this study conducts an exhaustive and up-to-date review of solar irradiance and solar power forecasting methods used in the literature. Although there are a plenty of review papers in the literature, differently, we have created the extensive and comparative literature tables considering very-short term, short-term, medium term and long-term forecasting periods in this study. Furthermore, we have examined each paper in terms of its input data, forecasting interval, forecasting model, forecasting accuracy and forecasting results. As a result of overall assessments, this study provides complete and considerable information about the current status and future prospects in solar irradiance and solar power forecasting.