After presenting the governing equation for topographic waves and discussing its properties and some known solutions in bounded and unbounded domains we point out an interesting and potentially useful connection between the spectrum of the topographic wave operator in a semi-infinite channel and that of the Schrodinger equation of an electron subject to the potential well. We then show that in closed basins there are three types of modal structures: global, basin-wide; small scale, basin-filled; localized. Effects of the variation of the topography on the dispersion relation are discussed and the influence of the curvature of an elongated basin on the dispersion relation and on the modal structure is studied. To further aid in the identification of the individual mode types in rectangular basins the current ellipses and the Stokes drift vectors are computed. A preliminary analysis of a double trench finally demonstrates how shelf waves may, through resonance, excite topographic waves in fjords or estuarine channels.