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Single-phase matrix converters (MCs) are undergoing rapid developments due to their bipolar voltage gain (as required in dynamic voltage restorers) and step-changed frequency operation (used in high step-up ac-dc rectifiers, and to provide medium frequency isolation in traction and wind turbine converters, etc.). However, existing buck-boost MCs require high-voltage/current rating devices, and suffer from large component voltage/current stresses and ripples, significantly degrading their efficiency. This article proposes a highly efficient single-phase buck-boost MC; consisting of eight IGBTs (implemented using two full-bridge IGBT modules), second-order input and output filters, and a small value film capacitor. Efficient discrete inverting and noninverting buck and boost operations are proposed (same as that of sixteen-switch cascaded buck-boost MC) with significantly lower component voltage/current stresses and ripples. In addition, flexible inverting and noninverting buck-boost operations are proposed with independent control of buck and boost duty ratios. All of the proposed operations are free of commutation issues, compatible with reactive loads, and provide smooth input and output currents. Furthermore, all the switches have same voltage stresses, and all four switches in a full-bridge module experience the same current stresses. A comprehensive description of circuit operation is presented based on a number of proposed switch modulation strategies with a nonunity power factor load, followed by design guidelines, and comparative evaluations with existing topologies. Finally, experimental verification results are presented, using a 400-VA laboratory prototype converter.