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Two-dimensional magnetic recording (TDMR) is a novel storage architecture that, in theory, can achieve a density of up to 10 Tb/in2. It uniquely differs from other proposed next-generation architectures because of its reliance on sophisticated 2-D signal-processing algorithms. Recently, a number of contributions have been made in the development of read-channel models and detectors for TDMR systems. In this paper, we provide a detailed review on all important read-channel models under consideration. Our discussion focuses on the purpose of each model, placing a special emphasis on the suitability of the Voronoi model for the purpose of designing detectors. We also propose several detection schemes for TDMR based on the Voronoi model and present some numerical results.