Branch-and-Cut combines branch-and-bound with cutting plane methods for solving integer programs. At each node of the branch-and-bound tree: (1) solve LP relaxation; (2) if fractional, generate and add cuts to strengthen bounds; (3) if still fractional, branch on fractional variable; (4) prune nodes using bounds and cuts. This synergy is more powerful than either method alone - cuts improve bounds throughout the tree, reducing enumeration. Modern implementations include: cut pools, cut selection strategies, branching rules, and preprocessing techniques. Branch-and-cut is the core technology in commercial solvers (CPLEX, Gurobi, SCIP) and has enabled solving previously intractable large-scale integer programs in routing, scheduling, and logistics.