Different solutions for far-field light shaping are reviewed. For design algorithms based on geometric optics, typically, a mapping between the irradiance distribution of the input and the target is assumed. In this thesis, the validity of the mapping assumption is analyzed from a physical-optics point of view. It is revealed that it is true only when all the operators in the system modeling are pointwise operators. With the physical-optics modeling techniques, a design strategy is provided that starts from a functional design and continues with a structural design. By applying the inverse method, the light-shaping problem is reduced to a Fourier pair synthesis. For the Fourier pair synthesis, a mapping-type algorithm is introduced in the homeomorphic case. In the proposed method, the solution of the mapping between the Fourier pair is integrable. Therefore, the output wavefront phase can be achieved in a single integration step. After designing the output wavefront phase, the functional embodiment is nothing other than a wavefront phase response (WPR) function. The structural design of light-shaping elements is developed with the obtained WPR function, or more directly with the output wavefront phase. The design of both a holographic optical element (HOE) and a freeform lens for light shaping is demonstrated. The element function of the HOE design is the same as the WPR function. The local grating model is then derived from its element function. A hybrid component by adding a curved surface to the HOE is suggested to reduce the grating effects from the HOE. For the design of a freeform lens, an algorithm is proposed that combines the output wavefront phase design and the construction of the freeform surface in an iterative way. The algorithm has no restriction about the input wavefront and the shape of the predefined surface. Moreover, the Fresnel effect of the freeform surface is also considered in the design.