Cutting Plane Methods solve integer programs by iteratively adding linear inequalities (cuts) that tighten the LP relaxation without removing integer feasible solutions. Starting with LP relaxation, if the solution is fractional: (1) identify violated valid inequalities; (2) add cuts to strengthen formulation; (3) resolve; (4) repeat until integer solution found or proven optimal. Types of cuts: Gomory cuts (derived from simplex tableau), cover inequalities, clique cuts, and problem-specific cuts. Pure cutting plane methods rarely work alone but are integrated into branch-and-cut algorithms - combining branching with cutting planes. Modern solvers (CPLEX, Gurobi) automatically generate various cut types for improved performance.