In this thesis work, I present three extensions of the Standard Model, corresponding to three independent attempts to improve our understanding of dark matter and Large Hadron Collider data in terms of new physics. The first work studies the chargino superparticle in the R-symmetric Minimal Supersymmetric Standard Model, an extension known to improve results regarding the hierarchy problem of the Minimal Supersymmetric Standard Model. In a regime where the lightest superparticles are the chargino and the gravitino, I explore the parameter space in order to determine collider-viable regions for their masses that simultaneously respect the 125 GeV Higgs and squark mass limits. The second work is a dark matter model where the dark candidate carries a flavor charge and couples to two scalar mediators. These two scalars are conventionally used in the Froggatt-Nielsen class of flavor models to explain the mass sizes and mixings of quarks and leptons. The trademark of the model is that dark matter reaches its abundance mostly through annihilation into a pair of distinct mediators, with meson mixing observables imposing stronger constraints than current direct detection prospects. The third model was designed as a means to reproduce the Higgs-to-tau-and-mu excess seen in the proton-proton collisions at the Large Hadron Collider. The approach involved four-fermion interactions between SM leptons and two different vectorlike fermions, which needed to be as heavy as tens-of-TeV in order to simultaneously satisfy such excess and the limits in other flavor-violating processes.