The necessity for a rational interpretation of scanning tunneling microscopy (STM) and atomic force microscopy (AFM) images is demonstrated by our recent STM/AFM studies of layered transition-metal chalcogenides, layered transition-metal halides, organic conducting salts, and alkanes adsorbed on graphite. To a first approximation, the STM image of a surface is described by the partial density plot rho(r0, e(f)) of the surface, and the AFM image by the total density plot rho(r0). The contribution of an atom to the rho(r0, e(f)) plot increases with decreasing distance to the tip and with increasing electronic contribution to the energy levels around the Fermi level. Since the atoms that protrude more do not necessarily make greater contributions to the energy levels near the Fermi level, it is difficult to achieve a rational interpretation of STM images unless appropriate partial density plots are calculated. For a variety of layered compounds, the STM and AFM images are well simulated by the rho(r0, e(f)) and rho(r0) plots calculated by the extended Huckel tight-binding electronic band structure method. Partial and total density plot calculations provide not only a basis for a rational interpretation of ideal STM and AFM images but also a step toward systematic studies of how dp-surface interactions and tunnelling conditions affect the images.