For advanced functional polymers such as biopolymers, biomimic polymers, brush polymers, star polymers, dendritic polymers, and block copolymers, information about their surface structures, morphologies, and atomic structures is essential for understanding their properties and investigating their potential applications. Grazing incidence X-ray scattering (GIXS) is established for the last 15 years as the most powerful, versatile, and nondestructive tool for determining these structural details when performed with the aid of an advanced third-generation synchrotron radiation source with high flux, high energy resolution, energy tunability, and small beam size. One particular merit of this technique is that GIXS data can be obtained facilely for material specimens of any size, type, or shape. However, GIXS data analysis requires an understanding of GIXS theory and of refraction and reflection effects, and for any given material specimen, the best methods for extracting the form factor and the structure factor from the data need to be established. GIXS theory is reviewed here from the perspective of practical GIXS measurements and quantitative data analysis. In addition, schemes are discussed for the detailed analysis of GIXS data for the various self-assembled nanostructures of functional homopolymers, brush, star, and dendritic polymers, and block copolymers. Moreover, enhancements to the GIXS technique are discussed that can significantly improve its structure analysis by using the new synchrotron radiation sources such as third-generation X-ray sources with picosecond pulses and partial coherence and fourth-generation X-ray laser sources with femtosecond pulses and full coherence.