Myxobacteria are a group of Gram-negative bacteria that act in a 'social' manner. This is most noticeable in the production of the fruiting bodies while cells are under starvation. The social aspect is also evident during swarming, or coordinated expansion of a colony with sufficient nutrient. In this thesis, both fruiting body formation and swarming of Myxobacteria are modeled. It is demonstrated that a modified Lattice Gas Cellular Automata model of cells with reversals is capable of aggregation and mounding in fruiting body formation. In the model, the amount of spores produced reaches a maximum at a reversal frequency similar to that found in experiments. Swarming of cells with A and S motility is also modeled as a modified lattice gas cellular automata, and S-motility in an off-lattice manner.