Understanding and coping with uncertainties in district heating systems: a multi-pathway review from probabilistic modeling to intelligent integration

District heating systems (DHS) are key infrastructures supporting urban energy transition and low-carbon development, which often operate under the influence of multiple interrelated factors and introduce various forms of uncertainties inevitably, potentially undermining energy efficiency and thermal comfort. Probabilistic methodology is recognized as one of the most mainstream mathematical tools for coping with uncertainties, providing mathematical pathways to describe, quantify, and reason about uncertainties. This paper provides a systematic review of mitigation strategies for various sources of uncertainty, including demand-side, network, supply-side, and coupled multi-source uncertainties, with particular emphasis on existing approaches that span the entire process from uncertainty characterization and decision-making to operational implementation, highlighting their strengths while also identifying their limitations. The critical role of probabilistic approaches is underscored in addressing uncertainty, while set-based techniques remain essential for worst-case guarantees, affirming their complementarity. The mainstream pathway for addressing uncertainty in DHS adopts a two-stage framework, in which the uncertainty set is first reduced through scenario clustering or interval bounding, and the remaining uncertainty is subsequently managed by robust or risk-averse optimization with manageable computational complexity. This paper further assesses emerging hybrid methodologies that synergistically incorporate probabilistic rigor, artificial intelligence (AI) driven adaptability, and coordinated multi-scale strategies. Advances in Fifth‑Generation District Heating and Cooling (5GDHC) networks and real‑time digital twins (DT) facilitate cyber‑physical uncertainty management at the device level. In the end, this paper offers guidance for future research and practical applications of probabilistic and these hybrid-driven strategies in sustainable practices.