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The increasing volume of connection requests for load and generation is putting pressure on the limited grid capacity of distribution networks (DNs), resulting in growing waiting lists. Consequently, distribution system operators (DSOs) are seeking fast and effective congestion management (CM) strategies to reduce delays and enable timely customer connections. In this paper, we present a comprehensive review of CM methods for DNs to assist DSOs in addressing this challenge. By taking into account the severity of customer impact, we categorize existing CM methods into four groups: (1) DSO-owned technical solutions, (2) tariff- and flexible contract-based solutions, (3) DSO-procured market-based solutions, and (4) DSO-direct interventions. Within DSO-owned solutions, we provide an in-depth review of network reinforcement and equipment control-based solutions. Next, we examine tariff and flexible contract-based solutions, including time-of-use (TOU) tariffs, TOU tariffs with incentives, dynamic tariffs and non-firm capacity contracts. The DSO-procured market-based solutions cover research on various market designs aimed at addressing congestion issues. Finally, we review DSO-direct interventions as last-resort approaches for CM. Additionally, we analyze research studies that propose underlying mathematical methods for CM, categorizing them into three groups: (1) deterministic analysis, (2) stochastic analysis, and (3) machine learning-based methods. For each study, we highlight key contributions along with our reflections on its applicability. For the most relevant methods, we also present simulation results to validate their working principles. Finally, we highlight future challenges in CM, offering insights for DSOs and researchers in developing effective CM solutions. • An extensive review of modern congestion management methods aimed at enhancing the integration of new generation and load is presented. • Current congestion management practices employed by distribution system operators (DSOs) are discussed in detail. • Existing research is classified into DSO-oriented groups: (1) DSO-owned technical solutions, (2) tariff and flexible contract based solutions, (3) DSO-procured market-based solutions, and (4) DSO-direct interventions, a classification inspired by the methods currently adopted by DSOs. • A review of the progress and remaining challenges in mathematical modeling for congestion management is also provided.