Quasars at high redshift (z > 6) are a 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. This talk will start with a brief description of the motivation for and history of high-z quasar surveys, and then presents our SHELLQs project, which looks for high-z quasars based on the Subaru Hyper Suprime-Cam imaging data. The project has so far found ~200 low-luminosity quasars, which have played a vital role in establishing the quasar luminosity function at z = 6 and z = 7. We have also identified possible new classes of high-z quasars, namely, dust-reddened quasars, cousins of narrow-line Seyfert 1s, and candidate obscured quasars, among the low-luminosity population. The talk will be concluded with future prospects, highlighting our own JWST program and future facilities such as Rubin LSST, Euclid, and Roman.