The Large Hadron Collider (LHC), a multinational experiment began running in 2009, is highly expected to discover new physics that will help us understand nature of the universe and begin to find solutions to many of the unsolved puzzles of particle physics. For over 40 years the Standard Model (SM) has been the accepted theory of elementary particle physics, except for one unconfirmed component, the Higgs boson. The LHC has recently discovered this Standard-Model-like Higgs boson. This discovery is one of the most exciting achievements in elementary particle physics. Yet, a profound question remains: Is this rather light, weakly-coupled boson nothing but a Standard Model Higgs or a first manifestation of a deeper theory? Also, the recent discoveries of neutrino mass and mixing, experimental evidences of dark matter and dark energy, matter-antimatter asymmetry, indicate that our understanding of fundamental physics is currently incomplete. For the next decade and more, the LHC and future colliders will be at the cutting-edge of particle physics discoveries and will shed light on many of these unanswered questions.
There are many promising beyond-Standard-Model theories that may help solve the central puzzles of particle physics. To fill the gaps in our knowledge, we need to know how these theories will manifest themselves in controlled experiments, such as high energy colliders. I discuss how we can probe fundamental physics at current and future colliders directly through searches for new phenomena such as resonances, rare Higgs decays, exotic displaced signatures, and indirectly through precision measurements on Higgs in this work. I explore beyond standard model physics effects from different perspectives, including explicit models such as supersymmetry, generic models in terms of resonances, as well as effective field theory approach in terms of higher dimensional operators. This work provides a generic and broad overview of the physics potentials of different particle physics experiments, supported by several detailed studies on characteristic physics cases to highlight the special features. The studies presented in this work provide timely and crucial knowledge highly demanded for our understanding and planning for future experiments.