Quasars at high redshift are an important and unique probe of the distant Universe, for understanding the origin and progress of cosmic reionization, the early growth of supermassive black holes, and the evolution of quasar host galaxies and their dark matter halos, among other topics. We will present the latest results from our SHELLQs (Subaru High-z Exploration of Low-Luminosity Quasars; arXiv:1603.02281) project, a new spectroscopic survey for low-luminosity quasars at z > 6. By exploiting the exquisite imaging data produced by the Subaru Hyper Suprime-Cam survey, we aim to probe quasar luminosities down to M1450 ~ -22 mag, i.e., below the classical threshold between quasars and Seyfert galaxies, over 1400 deg2. Candidate selection is performed by combining several photometric approaches including a Bayesian probabilistic algorithm. A large spectroscopic observing program is underway, using Subaru and other 8-10m telescopes; in particular, SHELLQs has been approved as a Subaru intensive program to use 20 nights in the coming four semesters. As of July 2016, we have discovered 22 quasars and 14 bright galaxies at z ~ 6 and beyond. This result indicates that we are starting to see the steep rise of the luminosity function of high-z galaxies, compared to that of quasars, at magnitudes fainter than M1450 ~ -22 mag or z(AB) ~ 24 mag. Multi-wavelength follow-up studies of the discovered objects as well as further survey observations are ongoing.