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Passive optical networks are a prominent broadband access solution to tackle the "last mile" bottleneck in telecommunications infrastructure. Data transmission over standardized PONs is divided into time slots. Toward the end of PON performance improvement, a critical issue relies on resource management in the upstream transmission from multiple optical network units (ONUs) to the optical line terminal (OLT). This includes resource negotiation between the OLT and the associated ONUs, transmission scheduling, and bandwidth allocation. This article provides an overview of the resource management issues along with the state-of-the-art schemes over time-division multiplexed PONs (TDM-PONs). We categorize the schemes in the literature based on their features, and compare their pros and cons. Moreover, we introduce a unified state space model under which all TDM-PON resource management schemes can be evaluated and analyzed for their system level characteristics. Research directions are also highlighted for future studies.