At the J-PARC muon facility (MUSE), new beamlines started operation recently. H-line is a high-intensity pulsed muon beamline for fundamental physics experiments. The first beam of the H-line was delivered to its first branch (H1 area) in January 2022, where a precise measurement of the muonium hyperfine structure and a search for μ-e conversion will be conducted. Further extension of the second branch of the H-line for a muon g-2/EDM experiment and a transmission muon microscope project is also ongoing. In addition, the second branch of the surface muon beamline (S2 area of the S-line) was opened for a muonium 1S-2S spectroscopy experiment in FY2021. In this paper, the recent upgrade and present status of the J-PARC muon facility and its prospects are presented.