This monograph deals with information-theoretic methods and analysis for developing two-dimensional constrained codes and signal processing algorithms for holographic memories. Though the applications of these theoretical ideas are aimed towards holographic memories, many of the techniques presented within this monograph are applicable to broader areas in science and technology beyond data storage. The key features of this monograph include:(1) Methods for computing capacity bounds for two-dimensional runlength-constrained channels with an eye towards designing two-dimensional codes.(2) An analysis of the holographic channel capacity and space-volume multiplexing tradeoffs for different holographic recording schemes for maximizing the volumetric storage density.(3) A study of the two-dimensional pixel misregistration problem and an algorithm for signal recovery.(4) Discussion of applications in other areas of science and engineering.