Abstract: Following a brief introduction of the development history of the supersonic commercial transport (SCT), the characters of several developing supersonic business jets are given. The conceptual design research of the small SCTs being served in the time period 2020-2035 and their possible configurations and features are described, too. Due to sonic boom reduction being one of the main tasks for developing SCT, some optimal design methods for reducing sonic boom are discussed in detail in the present paper, which are: the design method based on linearized theory; sonic boom mitigation method using inverse design of coupling Euler solver (Cart 3D) and adjoint method; the approach of advanced sonic boom prediction using augmented Burgers equation; the formulation that boom propagation and CFD are formally coupled for the purpose of obtaining gradients of a ground based objective with respect to the aircraft shape design variables; the optimization and adjoint-based CFD for the conceptual design of low sonic boom aircraft.