This thesis investigates certain fundamental problems in decentralized decision making and computation. We study the problem of whether a set of decision makers (or processors) with different (but related) information may make compatible decisions without communication and we characterize the computational complexity of this problem. We also analyze the complexity of other basic problems of decentralized decision making, such as decentralized detection (hypothesis testing). We then consider a scheme whereby a set of decision makers (processors) exchange and update tentative decisions which minimize a common cost function, given information they possess; we show that they are guaranteed to converge to consensus. Finally, we consider a broad class of asynchronous distributed (deterministic and stochastic) iterative optimization algorithms tolerating communication delays. We associate communication requirements with such algorithms and show that they converge appropriately under certain conditions which are no more severe than those required for their centralized counterparts. Several applications in human organizations, parallel computation and distributed signal processing are indicated. Additional keywords: decision theory. (Author).