Superconducting logic circuit families, which utilize a single flux quantum as a logical bit information has outstanding features in terms of operating speed and energy consumption. Two types of logic circuits are extensively researched at present: one is rapid single flux quantum (RSFQ) logic, which is driven by DC bias current, and the other is adiabatic quantum flux parametron (AQFP) logic, which is operated by AC bias current. The operating speed of the RSFQ logic is quite high and ranging 20 to 100 GHz, whereas the energy consumption of AQFP logic is extremely small and about 1 zJ per bit at 5 GHz clock frequency. In this talk, I will discuss how synchronous and asynchronous LSI design is conducted in superconducting logic circuits and what design issues we have in the future.