Transportation systems management and operations (TSMO) increasingly depends on timely interpretation of heterogeneous data, from various sensor streams, incident reports, traveler feedback, and visual observations. Large language models (LLMs), including emerging multi-modal large language models (MM-LLMs), provide a new mechanism for integrating these structured and unstructured inputs into operator-facing decision support. This survey paper reviews LLM- and MM-LLM-based applications in TSMO across three domains: transportation operations & services (supply), mobility & fleet services (demand), and data, modeling & decision support. Using a PRISMA-guided screening process, we synthesize current studies while distinguishing operationally oriented applications from prototype and emerging concepts. We further identify recurring challenges in data heterogeneity, real-time inference, explainability, multi-modal fusion, and governance. Finally, we outline existing gaps and future directions in localized adaptation, edge deployment, benchmarking, and cross-agency collaboration. Overall, LLM-based systems appear most promising as a decision-support layer, with MM-LLMs offering particular value when heterogeneous text, visual, and sensor inputs must be integrated.

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