Progress in understanding physical mechanisms for the excitation and maintenance of spiral structure has considerably benefited from investigations of tightly wound spiral density waves (e.g., see Bertin 1980). These studies have identified the existence of four basic kinds of density waves (trailing and leading waves, and in each case short and long waves) with different propagation properties. In addition, they have led to the conclusion that some realistic galaxy models can support self-excited global normal spiral modes. These owe their maintenance to the presence of trailing waves with opposite propagation properties and are excited mostly as a result of a WASER (superreflection) mechanism at corotation. In discussing the dynamics of spiral structure and in comparing theory with observations a number of important issues should be kept in mind (Lin and Bertin 1981). Here we just recall that the calculation of spiral modes is being pursued by many researchers, using different methods. In general the structure and the growth rates of the dominant modes are determined by the radial distributions of the active disk density, the differential rotation, and the dispersion speed through the dimensionless functions εo, j, and Q (Haass, Bertin and Lin 1982).