Packet scheduler is an important component of WiMAX MAC layer that helps to provide Quality of Service (QoS) guarantee to various service classes of WiMAX systems. Providing an in-depth understanding, analysis, and classifications of WiMAX scheduling schemes is of utmost importance toward designing effective practical schedulers. This article provides a comprehensive survey of various WiMAX scheduling schemes for both point-to-multipoint and multi-hop relay systems. We first discuss on an existing QoS architecture of conventional WiMAX systems, then we make a comprehensive classification and in-depth analysis of the current state-of-theart of single-and multi-hop relay systems which further classifies the scheduling schemes based on the use of channel state condition, queue state, and type of scheduling scheme. We also highlight detailed descriptions of various design aspects, objectives, methodologies, and limitations of the previously proposed researches. After extensively reviewing literatures on scheduling mechanisms, we found out that there still remain many issues and consideration in the previously scheduler designs. Hence, we discussed on the main important aspects related to schedulers design to assist researchers, network designers, and Internet Service Providers in designing effective practical schedulers for single-hop or multi-hop relay systems. Finally, the article concludes on the research gaps found in the previously discussed researches and outlines open research issues for future work.