This chapter describes how to simplify optimization problems by approximation and relaxation. Approximations include linearizations, convexifications, and problem-dependent simplifications. Relaxations are approximations that enlarge, not shrink, the feasibility region. We also explain how to generate an upper bound and a lower bound of the optimal value of the objective function of an optimization problem. Since approximations and relaxations are very much problem-dependent, we use a complex nonlinear and nonconvex but specific optimization problem to illustrate approximations via linearization, convexification, and others.