Network Flow Problems involve finding optimal flows through networks represented as directed graphs with arc capacities. Types include: (1) Maximum Flow - find maximum flow from source to sink respecting arc capacities (solved by Ford-Fulkerson, Edmonds-Karp, or Push-Relabel algorithms); (2) Minimum Cost Flow - route flow at minimum cost satisfying supply/demand constraints (solved by network simplex); (3) Multi-commodity Flow - handle multiple commodities with shared arc capacities. Applications span: transportation networks, telecommunications, supply chain management, and project scheduling. The max-flow min-cut theorem establishes duality between maximum flow and minimum cut capacity.