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The rapid diversification of energy sources has highlighted the limitations of traditional, independent single-carrier energy markets. As a result, the development of interactive multi-energy markets (IMEMs) has become a central trend in the global energy transition. This evolution, driven by emerging energy technologies, introduces substantial challenges across four dimensions: operational management, policy and regulation, business mechanisms, and carbon-related challenges. This review examines the commercialization pathways of emerging energy technologies, specifically focusing on hydrogen and carbon-related technologies, and explores their roles in addressing these challenges. It further emphasizes the critical role of energy management (EM) approaches in addressing the inherent complexities of multi-energy integration. Four representative EM approaches are analyzed, including optimal operation and scheduling, energy trading and market clearing, energy system planning, and economic optimization for performance. Each approach is systematically mapped to specific categories of challenges and further linked to system-level transition dimensions, elucidating their respective contributions to improving the market efficiency, flexibility, and sustainability. Finally, this review presents future research perspectives, highlighting the necessity for cross-market coordination models, multi-layered market designs, and integrated policy-technology frameworks. • Multi-energy market challenges are categorized into four dimensions—operational, policy, business, and carbon-related. • An analytical framework is established to map energy management (EM) approaches to the four categories of challenges in interactive multi-energy markets. • Commercialized hydrogen and carbon technologies in energy management is analyzed. • EM approaches are reviewed and mapped to the corresponding challenge dimensions to reveal their specific contributions.