Bacterial chemotaxis is the behavior of bacteria to swim towards favorable chemical locations, while away from unfavorable ones. The ternary complex, which is comprised of the transmembrane methyl accepting chemotaxis protein (MCP), the coupling protein CheW and the kinase CheA, is essential to the signaling pathway. The regulation of CheA by MCPs determines the rotation bias of the flagella and hence the movement of the cells. The exquisitely high sensitivity and signal amplification of chemotaxis is attributed to the architecture of individual complexes and their assembly into larger arrays. This dissertation focuses on the study of the ternary complex using various biophysical methods. We determined the first crystal structure of the ternary complex in Thermotoga maritima. The components in the complex crystal structure are well conserved among bacteria and therefore we believe this architecture is likely to be commonly preserved. We proposed a model on the assembly of the complex arrays from individual complex based on this crystal structure and the electron cryotomography findings by our collaborators. We also determined a crystallographic dimer structure of the coupling protein CheW. Based on this dimer structure of CheW as well as a previously determined crystallographic dimer structure of the regulatory domain of CheA, we suggest other possible ways of that the receptor arrays may assembly. We also designed and obtained cytoplasmic regions of MCPs associated by a trimerization motif. These designed "trimers-of-receptor-dimers" form a stimulatory complex with CheA and CheW. We probed the conformation of the resulted stimulatory complex and compared it with the conformation of the previously characterized inhibitory complex.