Abstract The luminosity of a spiral arm is believed to originate primarily from the very young, newly forming stars; and the spiral arm itself is believed to be a spiral wave which is capable of triggering the formation of the young stars selectively along the wave crest. Such a wave has been visualized from two different viewpoints: first, the density wave viewpoint in which gravitational forces are considered as dominant forces, with magnetic forces also playing a role but of secondary importance; and second, the hydromagnetic wave viewpoint in which magnetic fields are visualized as the dominant forces in the gas. At the present time, only the density wave viewpoint has been developed toward a coherent theory to provide a quantitative viewpoint from which to visualize spiral structure. In the density wave model, a galactic shock wave forms in the gaseous component of the galactic disk as a necessary consequence of the theory of waves for sufficiently large amplitudes and is the nonlinear counterpart of the small amplitude, linear density wave. The galactic shock wave is visualized as a possible triggering mechanism for the gravitational collapse of gas clouds, leading to star formation along a spiral arm. In the density wave model for galaxies which undergo sizeable differential rotation, a shock, a sharp H I gas peak, a narrow dust lane, and the strongest magnetic fields are predicted to lie in a narrow lane on the inner side of the bright optical arm of young stars and H II regions triggered into existence in the shock. Recent observational results from the high resolution Westerbork Synthesis Radio Telescope in the Netherlands indicate that one striking example which exhibits such features as these is the galaxy M 51. Other theoretical results have been determined with the density wave model, and a number of these have been confirmed through observational studies. For example, several spirals studied to date are found to have neutral hydrogen gas concentrated along the optical spiral arms and systematic motions which correspond to the systematic motions expected for density waves. For our own Galaxy the shock wave together with the differential rotation of the gas provides a natural explanation for the striking separation between the peaks of the abundance distributions of H II gas and H I gas. The distinction between narrow optical arms and broad optical arms in the density wave model is found to depend on whether the velocity component of basic rotation normal to a spiral arm is greater than or less than the acoustic speed of the gas, and this distinction may explain why some galaxies have narrow optical arms while other galaxies have broad optical arms. From a recent study of the density wave models for twenty-five external galaxies, it is found that those galaxies whose models predict the possibility for strong shock waves exhibit long, well-developed spiral arms, and those galaxies whose models predict weak shock waves exhibit less developed spiral structure. On the small scale, a physical picture for star formation is evolving based on the two-phase model for the interstellar medium. Galactic shocks are initiated in the hot intercloud phase, and the cold clouds are viewed simply as embedded bodies which expand or contract to adjust to changes of the ambient pressure of the intercloud phase. The pressure increase across the galactic shock occurring in the intercloud phase is in turn transmitted to the cold clouds, leading to star formation. To be sure, much further work needs to be done to suggest further physical results applicable to the physical phenomena and physical processes which occur in galaxies and to investigate those areas where unresolved questions and exciting problems still remain.