In this chapter, the fundamental characteristics of ocean waves, including their motion, classification, and deformation, are discussed. The linear and nonlinear wave theories and their implications were then summarized. The mathematical model was provided to estimate the wave energy potential. The mechanism by which the wave delivers its energy to the wave energy converter is discussed. Then, the governing hydrodynamic equations for a PA-WEC were modeled, including excitation forces, radiation losses, PTO forces, and hydrostatic forces. The importance of the floater geometry and its resonance characteristics for designing an optimal PA-WEC is discussed. The computational methods, including both frequency-domain and time-domain simulations, are introduced. The literature review highlighted recent floater geometries, limitations in existing PA-WEC designs, and the need for innovative floater geometries and scaling methods.