The hypothesis of quasi-stationary spiral structure in galaxies was explicitly formulated in the early 1960's in papers of Bertil Lindblad and of Lin and Shu. It asserts that the grand design observed in spiral galaxies may be described by the superposition (and interaction) of a small number of spiral modes. (See Lin and Bertin, 1981 for a fairly extensive review of the theory.) We wish to re-affirm the correctness of this hypothesis in the present contribution. Early numerical experiments by P.O. Lindblad and by Miller, Prendergast and Quirk demonstrated that spiral structures occur naturally in certain models of stellar systems, although it was difficult to control the morphological types of galaxies simulated. We are now able to simulate galaxies of various morphological types in a controllable manner. Numerical fluid-dynamical codes developed by Pannatoni (1979) and improved by Haass (1982) have been used to calculate normal modes of various spiral types (Haass, Bertin, and Lin 1982) in the morphological classification of Hubble, Sandage, and de Vaucoulers. Furthermore, the processes that govern the maintenance and the excitation of these modes simulating both normal spirals and barred spirals, can be understood by using analytical theories which are closely related to the local dispersion relationship, as Bertin will describe in his paper at this conference. Understanding these mechanisms enables us to choose the parameters and the distribution functions in our models more properly in order to exhibit the desired characteristics in the computed modes. Such an approach also has important implications on observational studies. Much of the previous work on comparison between theory and observations in normal spirals used only the short trailing waves. A mode must consist of at least two waves propagating in opposite directions. It has been found that, at least in normal spiral modes, the long wave branch provides essentially only a modulation of the amplitude along the short wave branch, which accurately describes the phase. Previous calculations are thereby justified. [These points were not adequately covered in the previous paper reviewing theory of spiral modes.]