The explosive growth of the traffic between data centers has led to an urgent demand for high-performance short-reach optical interconnects with data rate beyond 100G per wavelength and transmission distance over hundreds of kilometers. Since direct detection (DD) provides a cost-efficient solution for short-reach interconnects, various advanced modulation formats have been intensively studied to improve the performance of DD for high-performance short-reach optical interconnects. In this paper, we report the recent progress on the advanced DD modulation formats that provide superior electrical spectral efficiency (SE) and transmission reach beyond that of simple direct modulation (DM) based direct detection (DM/DD). We first provide a review of the current advanced modulation formats for high-performance short-reach optical interconnects. Among these formats, Stokes vector direct detection (SV-DD) achieves the highest electrical spectrum efficiency, presenting itself as a promising candidate for future short-reach networks. We then expound some novel algorithms to achieve high-performance SV-DD systems under severe impairments of either polarization mode dispersion (PMD) or polarization dependent loss (PDL).