In Chapter 7 approximate solutions to the radiative transfer problems were discussed, and in Chapter 8 these solutions were used to examine the role of radiation in climate. Analyses of data obtained by sensors deployed at the surface of the Earth, on aircraft or balloons in the atmosphere, on platforms in the ocean, or on satellites in space, require more accurate methods, which are presented and discussed in this chapter. A class of more sophisticated approximation techniques is considered that are capable of approaching the exact solution as closely as desired. This class includes the discrete-ordinate method, the spherical-harmonic method, and the doubling-adding method. It is shown that “to the lowest order” the first two methods become the two-stream approximation, and the Eddington approximation, respectively. The close relation between the discrete-ordinate method and the doubling-adding method is also discussed.