The Muon Science Establishment (MUSE) is one of the major experimental facilities, along with those for neutron, hadron and neutrino experiments, in J-PARC. It makes up a part of the Materials and Life Science Experiment Facility (MLF) that hosts a tandem neutron facility (JSNS) driven by a single proton beam. The facility consists of a superconducting solenoid (for pion confinement) with a modest-acceptance (about 45 mSr) injector of pions and muons obtained from a 20 mm thick edge-cooled stationary graphite target, delivering a 'surface muon' beam (μ(+)) and a 'decay muon' beam (μ(+)/μ(-)) for a wide variety of applications. It has recently been confirmed that the beamline has the world's highest muon intensity (∼10(6) μ(+)/s) at a proton beam power of 120 kW. The beamline is furnished with two experimental areas (D1 and D2) at the exit branches, where an apparatus for muon spin rotation/relaxation experiments (μSR) is currently installed at the D1 area while test experiments are conducted at the D2 area. In this paper, the current performance of the MUSE facility as a whole is reviewed. The facility is still in the early stage of development, including both beamlines and infrastructure for experiments, and plans for upgrading it are discussed together with perspectives for research works envisaged with unprecedented high-intensity muons.