Major hurricanes are becoming more frequent due to climate change and the warming of the oceans. Now more than ever, the ability to model hurricanes accurately and provide advanced warning to affected areas is crucial. However, while hurricane track forecasting has greatly improved, there has been little improvement in intensity forecasting, partly due to inadequate observations and modeling of the inner core of the storm. CYGNSS, an experimental NASA satellite mission launched in December 2016, is designed to frequently measure surface wind speeds in hurricanes via GPS reflections. These additional measurements should improve forecasting of hurricane rapid intensification. This dissertation looks at new ways to use and interpret remotely sensed wind speeds in hurricanes. First, we look at how estimated storm intensity is affected by the spatial resolution of the satellite. Satellite-measured wind speeds are not point measurements—a single measurement is of a broad area on the surface where contributions from each part of the surface are given weight according to the antenna pattern. Hurricane intensity is usually determined by the maximum wind speed (Vm). Because satellite-measured wind speeds are effectively averages over a large area, the satellite-measured Vm is lower than the true Vm. Unless this is corrected for, hurricane wind fields from satellites will systematically underestimate storm intensity. This work explores how information from any satellite-measured wind field can be used to improve the estimated storm intensity via a scale factor correction. Next, hurricane parametric wind speed models are examined. Parametric wind models are established using meteorological principles combined with simplifying assumptions about the environment or storm structure. These models tune several free parameters to wind speed measurements by minimizing the difference between the measurements and the wind field “seen” by the model. Parametric wind models are especially useful for filling in gaps between measurements—once the free parameters are optimized, the model can report a wind speed estimate everywhere in the storm. Hurricane wind field characteristics such as Vm, radial distance to Vm, azimuthal information, and more are easily determined from a full wind field but are more difficult to estimate from a gap-filled wind field. Also, many modeling applications are enabled by having a full wind field. This dissertation discusses limitations of existing parametric wind models, and new parameters are added to allow for improved representation of a wider variety of storms. A parametric wind model is then used to find the center location of a hurricane using the principle that the model fit is best when the correct storm center is assumed. The storm center is the location that optimizes the model fit. Most storm center fixes are done manually—this is one of few automated storm center fix techniques and the only one not using cloud structure seen in satellite imagery. Accurate storm center locations are necessary for forecasting hurricanes, hurricane research, and historical record keeping. Lastly, a new CYGNSS data product is described which reports gridded surface wind speeds with increased convenience and reliability for users of hurricane-specific data. This product, which will be released to the public in early 2021, processes the CYGNSS wind speeds in a way that allows for self-consistency checks of the data. This new CYGNSS hurricane wind speed product is shown to be in excellent agreement with wind speeds from models and a well-established satellite.