Forecasting is one of the enabling technologies for the integration of weather-dependent renewable resources (e.g., solar and wind) into the electric grid. Accurate forecasts can reduce operational costs associated with intra-day variability, reduce imbalance charges incurred by plant operators due to inaccurate energy bids, decrease utility costs associated with day-ahead scheduling (thereby reducing overall O&M costs), as well as assist grid operators with balancing energy demand schedules. As the market penetration of solar-based power generation continues to grow, accurate and reliable forecasting techniques become increasingly more important. In this work, two key areas of solar forecasting are advanced. First, we develop intra-day (>1-hour) and day-ahead (>24-hour) forecasting methods to directly predict the generation of operational solar power plants, without the need for intermediate solar irradiance forecasts and resource-to-power modeling. Here we take a data-driven approach, leveraging Machine Learning (ML) techniques and publicly available, spatially resolved meteorological and remote sensing datasets. The proposed methods are analyzed and validated using two grid-connected 1 MW photovoltaic (PV) power plants in California. Second, we develop a method to directly and efficiently estimate cloud optical properties from longwave remote sensing data. The output of solar-based power generation systems is strongly dependent on cloud cover and optical depth, but in most solar forecasting methodologies cloud optical properties are over-simplified due to a lack of real-time, accurate estimates. The proposed estimation method builds upon a two-stream, spectrally resolved infrared radiation model coupled with high-resolution (5-minute, 2 km) spectral satellite imagery. We show that the proposed method can provide real-time, accurate estimates of cloud optical depth (COD) and cloud top height for all-sky (clear or cloudy) conditions during both daytime and nighttime.