Two-dimensional (2D) atomic crystals are attractive for use in next-generation nanoelectronics, due to their unique performances, which may lead to the resolution of the technological and fundamental challenges in semiconductor industry. Based on the introduction of 2D atomic crystal-based transistors and ambipolar behavior, the review presents a brief summary of 2D atomic crystal integration circuits, including memory, logic gate, amplifier, inverter, oscillator, mixer, switch and modulator. The devices show promising performances for the application in future nanoelectronics. In particular, the 2D atomic crystals, such as graphene, demonstrate good compatibility with the existing semiconductor process. The quaternary digital modulations have been achieved with flexible and transparent all-graphene circuits. Moreover, the heterojunction based on 2D atomic crystals may enable new devices beyond conventional field-effect transistors. The results make us be optimistic that practical 2D atomic crystal technologies with complex functionality will be achieved in the near future. Therefore, 2D atomic crystals are paving new ways for nanoelectronics.