Hard diffraction in proton collisions, where the initial state proton emerges from the interaction rather undisturbed despite a hard interaction scale, has been studied for a few decades. First observed in proton-proton collisions, the phenomenon is seen as well in deep inelastic electron-proton scattering (DIS) as a leading final state proton and a rapidity gap-region without final state particles. Although a rather successful description in terms of the exchange of a hadronic color singlet pomeron with a parameterized gluon content exists, it is still an open question whether a theoretically more well-founded description can be obtained based on quantum chromodynamics. The soft color interaction model (SCI) attempts this through additional gluon exchanges at momentum scales below the conventional scale of perturbative QCD and the hadronization scale. Such gluons can lead to an effective color singlet exchange and therefore to diffraction. This thesis explores the phenomenology of the SCI model in diffractive W and photon+jet production. For diffractive deep inelastic scattering, a dynamic color screening model is developed based on a summed amplitude for soft gluon exchanges. The studies of the model within Monte Carlo event simulation show that the additional dynamics improve the description of electron-positron scattering data from HERA. Dijet events in proton-proton collisions with an upper limit on the energy flow between the jets is sensitive to large angle gluon emissions. This thesis applies a resummation method which takes into account also secondary emissions to describe this observable and shows that a good description of data from ATLAS can be achieved. Supersymmetric extensions to the Standard Model provide a possible explanation for dark matter in the universe. The next-to-minimal supersymmetric extension (NMSSM) can contain a dark matter candidate in form of the lightest neutralino with a substantial singlino component. This thesis studies the prospects for indirect detection of dark matter for such viable NMSSM model points via the observation of neutrinos from neutralino annihilation in the sun with IceCube and the future extension PINGU. It is shown that with a few years of data taking large parts of the parameter space can be excluded or a discovery be made.