This thesis is a study of two-dimensional bursty channels from the information- theoretic as well as the coding-theoretic points of view. An information-theoretic model of bursty channels is defined and analyzed using probabilistic arguments. Two-dimensional burst correcting codes are developed. Their combinatorial and algebraic structures are examined. Two-dimensional bursty channels are used to model computer memories. The results of this thesis give bounds on the storage capacities of computer memories if sophisticated codes are used.