We review several existing approaches for the design of parallel binary decentralized detection architectures. Such architectures employ a bank of n parallel binary local detectors (LDs) and a Data Fusion Center (DFC). The kth LD compresses its local observations yk with a local decision rule Γk() into a local decision, uk, and sends it to the DFC. The DFC collects all local decisions U, U = lu1, u2,..., unr, and fuses them into a global decision, u0, using a global fusion rule Γ0(). When the local observations at the local detectors are statistically independent conditioned on the hypothesis, both the local decision rule and the global fusion rule become likelihood ratio tests (LRTs). Some architectures allow for possible feedback from the decision of the DFC (back into itself or into the LDs). There are several alternatives for the design of such systems. We review several architectures without and with feedback, and discuss design alternatives. These include fixing the local decision rule (without feedback  or with feedback ); solving simultaneously for the local decision rule and the global fusion rule (without feedback  or with feedback ); solving exhaustively for the local decision rule and the global fusion rule when the number of alternatives is finite and small ; and solving for the local decision rule and the global fusion rule with feedback by using one of several greedy scheme (e.g., ). The discussion highlights the tradeoff between performance and design complexity of parallel decision fusion systems.