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Metal-oxide-semiconductor field effect transistors (MOSFET) based on two-dimensional (2D) semiconductors have attracted extensive attention owing to their excellent transport properties, atomically thin geometry, and tunable bandgaps. Besides improving the transistor performance of individual device, lots of efforts have been devoted to achieving 2D logic functions or integrated circuit towards practical application. In this review, we discussed the recent progresses of 2D-based logic circuit. We will first start with the different methods for realization of n-type metal-oxide-semiconductor (NMOS)-only (or p-type metal-oxide-semiconductor (PMOS)-only) logic circuit. Next, various device polarity control and complementary-metal-oxide-semiconductor (CMOS) approaches are summarized, including utilizing different 2D semiconductors with intrinsic complementary doping, charge transfer doping, contact engineering, and electrostatics doping. We will discuss the merits and drawbacks of each approach, and lastly conclude with a short perspective on the challenges and future developments of 2D logic circuit.