In this paper we present an assessment of the status of models of the global solar wind in the inner heliosphere. We limit our discussion to the class of models designed to provide solar wind forecasts, excluding those designed for the purpose of testing physical processes in idealized configurations. In addition, we limit our discussion to modeling of the ambient wind in the absence of coronal mass ejections. In this assessment we cover use of the models both in forecast mode and as tools for scientific research. We present a brief history of the development of these models, discussing the range of physical approximations in use. We discuss the limitations of the data inputs available to these models and its impact on their quality. We also discuss current model development trends. Key Points Presents a review of the history, current status, and prospects for models of the ambient solar wind The review covers model quality from the perspective of both operational forecasting and scientific research support The review anticipates model and data input improvements expected over the next decade