The next-generation Wireless Metropolitan Area Networks, using the Worldwide Interoperability for Microwave Access (WiMAX) as the core technology based on the IEEE 802.16 family of standards, is evolving as a Fourth-Generation (4G) technology. With the recent introduction of mobility management frameworks in the IEEE 802.16e standard, WiMAX is now placed in competition to the existing and forthcoming generations of wireless technologies for providing ubiquitous computing solutions. However, the success of a good mobility framework largely depends on the capability of performing fast and seamless handovers irrespective of the deployed architectural scenario. Now that the IEEE has defined the Mobile WiMAX (IEEE 802.16e) MAC-layer handover management framework, the Network Working Group (NWG) of the WiMAX Forum is working on the development of the upper layers. However, the path to commercialization of a full-fledged WiMAX mobility framework is full of research challenges. This article focuses on potential handover-related research issues in the existing and future WiMAX mobility framework. A survey of these issues in the MAC, Network and Cross-Layer scenarios is presented along with discussion of the different solutions to those challenges. A comparative study of the proposed solutions, coupled with some insights to the relevant issues, is also included.