To cope with the exponential growth of the Internet traffic, optical communications has advanced by leaps and bounds. For several decades, Intensity modulation with direct detection (IM-DD) dominates the commercial short-reach optical communications. However, when upgrading the data-rate distance product to 1000 Gb/s·km per wavelength and beyond, IM-DD faces severe performance barrier. Aiming to improve the electrical SE and extend the transmission distance, advanced DD modulation formats have been proposed through a so-called self-coherent (SCOH) approach, where a carrier is transmitted together with the signal to achieve a linear mapping between the electrical baseband signal and the optical field. In that way, the impact of the CD can be removed from the received signal, greatly extending the transmission distance of the DD system. Particularly, Stokes-vector direct detection (SV-DD) has been proposed to realize linear complex optical channels as well as enhance the electrical spectral efficiency and transmission reach. In this talk, we present the principle and discuss the performance of SV-DD systems.