An overview of the RIKEN-RAL Muon Facility is reported. The RIKEN-RAL Muon Facility has been established at the Rutherford-Appleton Laboratory in the UK in 1992 and started to be in used for material science studies from 1994 by applying intense pulsed muon beams. More than 380 publications have been published in international journals and more than 100 domestic and international collaborations have been organized. As an example of those collaborative studies, a preliminary result of one recent experimental study on the magnetism in gold nano-cluster is reported. Additionally, a recent computational result on a local effect induced by an injected muon is reported in order to show how the presence of the muon leads to a local deformation of the crystal structure, thus changing the muon’s own position in finding the final stopping site self consistently.