In the past decade, there has been a substantial increase of grid-feeding photovoltaic applications, thus raising the importance of solar electricity in the energy mix. This trend is expected to continue and may even increase. Apart from the high initial investment cost, the fluctuating nature of the solar resource raises particular insertion problems in electrical networks. Proper grid managing demands short- and long-time forecasting of solar power plant output. Weather modeling and forecasting of PV systems operation is focused on this issue. Models for predicting the state of the sky, nowcasting solar irradiance and forecasting solar irradiation are studied and exemplified. Statistical as well as artificial intelligence methods are described. The efficiency of photovoltaic converters is assessed for any weather conditions. Weather modeling and forecasting of PV systems operation is written for researchers, engineers, physicists and students interested in PV systems design and utilization.