There is an increasing need to power cellular base stations (BSs) using solar energy in many parts of the globe. This is primarily because of the high cost of running these base stations on traditional power sources such as diesel due to lack of reliable grid availability in those areas. Apart from the high cost, the increasing diesel consumption also causes harm to the environment due to its increasing global carbon footprint. Using solar energy powered base stations is a highly promising solution to address these issues. One of the main areas of concern for solar powered cellular networks is to precisely manage the resources, namely, the available spectrum and energy so as to avoid power outages and to maintain an acceptable Quality of Service (QoS) for the end users. This article gives an overview of the challenges faced in resource management for solar powered base stations and presents state-of-the-art resource management strategies for both grid-connected and off-grid solar powered base stations.