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We review the modeling progress of the magnetic response of hard type-II superconductors (SCs) using the critical-state model (CSM). We focus on magnetization loops when a uniform field is applied to the SC and on the levitation forces that appear when the applied field is nonuniform. Different analytical and numerical solutions of the CSM are discussed, and the main characteristics and parameters of the magnetization loops and levitation forces are reviewed. Although this paper does not pretend to be an exhaustive review of the modeling of type-II SCs or of the superconducting levitation studies, a general overview of some important theoretical models used to understand the hard type-II SC macroscopic behavior is presented.