More than a decade after the discovery of the Higgs boson, the study of the Higgs boson remains a core research topic at the CERN LHC. Although much has already been learned about this particle, we are continuing to make new advances in this area of research. In this seminar I will discuss studies of the Higgs boson since its discovery, covering the recent status of Higgs boson precision measurements and searches. The prospects for Higgs boson physics with the data still to be collected during the remainder of the LHC and high-luminosity LHC programme will also be discussed briefly.