The discovery of the Higgs boson at the CERN Large Hadron Collider (LHC) in 2012 has filled in the last missing piece of the Standard Model. Yet we would like to know where the next physics scale above the electroweak scale lies. In this thesis, I focus on two directions to search for possible new physics beyond the Standard Model: the Higgs boson and the dark matter. As the recently discovered Higgs boson may serve as a lamppost for new physics search, it is of great importance to scrutinize its properties and look for possible deviations from the Standard Model. In particular, we study the Higgs boson rare decays to a pair of fermions associated with a photon and its observability at the LHC, and exploit  to probe the charm-quark Yukawa coupling. On the other hand, the existence of the dark matter has been well-established via many astronomical observations, in spite of its unknown particle origin. The TeV scale naturally appears if we assume that the correct dark matter abundance is achieved via thermal freeze-out with interaction strength of electroweak force, which is known as the “WIMP miracle”. It is crucial to search for such dark matter particles at the colliders. Future high-energy colliders provide excellent envi-ronments not only for discovering such particles but also for examining its properties such as spin and coupling structure. We study the search strategies and the observability of weakly interacting massive par-ticles with compressed spectra at the future colliders, and exploit single-photon processes and antler-topology processes to determine not only the spins but also the coupling structures at future high-energy colliders.