This thesis reports the latest measurements on one of the leading dark matter searches conducted by the Compact Muon Solenoid (CMS) experiment at CERN, leading to some of the most stringent constraints on hypothesized interactions between the Higgs boson and dark matter. The thesis also includes further research about the future outlook of the experiment, including exploratory research on the adaptation of deep learning models in future dark matter analyses to improve analysis sensitivity, and the design of a new type of data processing hardware to be used in the next phase of the CMS experiment.