The inversion problem for almost periodic media is considered and formulated. By use of a priori knowledge and the characteristics of the scattering data, two distinct inversion methods are found for determining almost periodic profiles from the scattering data. This is useful and important since almost periodic functions provide a convenient basis for expanding the characteristic functions of a variety of periodic, quasi-periodic, aperiodic, or random media. In addition, rational function reflection data lead naturally to generalized almost periodic profiles. These concepts are illustrated by several numerical examples.