Distributed solar generation is rising rapidly due to a continuing decline in the cost of solar modules. Most residential solar deployments today are grid-tied, enabling them to draw power from the grid when their local demand exceeds solar generation and feed power into the grid when their local solar generation exceeds demand. The electric grid was not designed to support such decentralized and intermittent energy generation by millions of individual users. This dramatic increase in solar power is placing increasing stress on the grid, which must continue to balance its supply and demand despite the potential for large solar fluctuations. To address the problem, this thesis proposes new data-driven techniques for better controlling, modeling, and forecasting residential solar power. The grid currently exercises no direct control over its connected solar capacity, but instead indirectly controls it by regulating new solar connections. This approach is highly inefficient and wastes much of the grid's potential to transmit solar. Instead, we propose Software-defined Solar-powered (SDS) systems that dynamically regulate solar flow rates into the grid and design an SDS prototype, called SunShade. Specifically, we introduce a new class of Weighted Power Point Tracking (WPPT) algorithms, inspired by Maximum Power Point Tracking (MPPT), capable of dynamically enforcing both hard and relative caps on solar power, which enables the grid to decouple rate control from admission control. In contrast, to avoid grid regulations entirely, homes can also partially or entirely defect from the grid to fully utilize their solar power without restrictions. We present a switching architecture that enables homes to dynamically switch between a local generator, battery, and solar to co-optimize their cost, carbon footprint, switching frequency, and reliability. We introduce switching policies that reveal a tradeoff between solar utilization and reliability, such that higher solar utilization requires more switching, which can lead to lower reliability. Enabling better control of intermittent solar also requires improving solar performance models, which infer solar output based on current environmental conditions. Recent solar models primarily leverage data from ground-based weather stations, which may be far from solar sites and thus inaccurate. In addition, these weather stations report cloud cover---the most important metric for solar modeling---in coarse units of oktas. Instead, we propose developing solar models based on data from a new generation of Geostationary Operational Environmental Satellites (GOES-16 and GOES-17) that began launching in late 2017. We develop physical and machine learning (ML) models for solar performance modeling using both derived data products released by the National Oceanic and Atmospheric Administration (NOAA), as well as the satellites' raw multispectral data. We find that ML-based models using the raw multispectral data are significantly more accurate than both physical models using derived data products, such as Downward Shortwave Radiation (DSR), and prior okta-based solar models. The raw multispectral data is also beneficial since it is available at much higher spatial and temporal resolutions---1km^2 and every 5 minutes---than oktas---25km^2 and every hour. The accuracy of our ML-based models on multispectral data is also better regardless of whether they are locally trained using data only from a particular solar site or globally trained using data from many solar sites. Since global models can be trained once but used anywhere, they can also enable accurate modeling for sites with limited data, e.g., newly installed solar sites. Solar forecasting models, which predict future solar output based on environmental conditions also help in better solar control. Accurate near-term solar forecasts on the order of minutes to an hour are particularly important because homes and the grid must be able to adapt to large sudden changes in solar output. Current solar forecasting techniques, which primarily use Numerical Weather Predictions (NWP) algorithms, mostly leverage physics-based modeling. These physics-based models are most appropriate for forecast horizons on the order of hours to days and not near-term forecasts on the order of minutes to an hour. While there is some recent work on analyzing images from ground-based sky cameras for accurate near-term solar forecasting, it requires installing additional infrastructure. We instead propose a general model for solar nowcasting from abundant and readily available multispectral satellite data using self-supervised learning. Specifically, we develop deep auto-regressive models using convolutional neural networks (CNN) and long short-term memory networks (LSTM) that are globally trained across multiple locations to predict raw future observations of the spatio-temporal data collected by the recently launched GOES-R series of satellites. Our model estimates a location's future solar irradiance based on satellite observations, which we feed to a regression model trained on smaller site-specific solar data to provide near-term solar photovoltaic (PV) forecasts that account for site-specific characteristics.