The COMET experiment is designed to search for a muon to electron ($\mu$-$e$) conversion with- out associating neutrinos, where the lepton flavour is violated at the charged lepton sector. The charged lepton flavour violating processes (CLFV) are forbidden in the Standard Model, while many plausible models beyond the SM (BSM) predict the detectable rates of CLFV processes. Therefore the CLFV searches are strong tools to probe the BSM. If any of CLFV process is discovered, it would be the clear evidence of BSM. The aim of the COMET experiment is to search for the $\mu$-$e$ conversion with a four orders of magnitude better sensitivity than the present upper limit. The experiment adopts the staging approach and the first stage of COMET is under construction at J-PARC/Japan, to search for the $\mu$-$e$ conversion with the intermediate sensitivity, $3\times10^{−15}$ in the early 2020s, followed by the Phase-II experiment to achieve the 100 times further improved sensitivity. We recently measured the quality of proton beam at J-PARC and it satisfied our exceedingly strict requirement. Preparations for the beam-line, detectors and electronics are intensively progressing on schedule. In addition, we recently started further optimisations for Phase-II experiment to improve the target sensitivity by factor 2–10 from the current baseline design, $3\times10^{−17}$. In this paper, the current status of the COMET experiment, mainly focusing on the recent highlights those of above mentioned are summarised together with future prospects.