In this thesis, we review the basics of phenomenology in particle physics at neutrino beam dump experiments and hadron colliders. We then consider the phenomenology of various new particles, with masses between 1 MeV and 1 TeV, at the intensity and energy frontiers. We perform sensitivity analyses for physics beyond the standard model at particle colliders (LEP and LHC) and a number of past and future neutrino beam dump experiments (SHiP, DUNE, LSND, MicroBooNE, MiniBooNE and SBND). In particular, we motivate searches for new heavy neutral leptons in single photon events at neutrino and collider experiments (and also via supernova cooling), millicharged particles in single electron events at neutrino experiments, lepton flavor violating scalars via standard model induced mixed flavor neutrino trident production at neutrino experiments, and colored scalar doublets at colliders in events with many jets, soft leptons and low missing energy. In the process, we set novel new bounds on the parameters of these theories and propose powerful new searches that can be performed. We also motivate the construction of a new detector at the LHC called milliQan, and perform a full Geant4 simulation to calculate its projected sensitivity for millicharged particles. The milliQan experiment has since been approved and is currently undergoing construction. / Thesis / Doctor of Philosophy (PhD) / In this thesis, we review the basics of particle physics at neutrino experiments and particle colliders. We then motivate and develop key searches that can be performed to look for new particles at a series of existing and future experiments. We focus on new particles with masses between the electron mass and 1000 times the proton mass. The many searches we consider involve looking for processes that produce a single ray of light, a single electron, a pair of oppositely charged "electron-like" events, new collider signatures, and/or modifications of star explosions. In the process, we set novel new bounds on many theories. We also motivate the construction of a new detector at the Large Hadron Collider called milliQan, and perform a full simulation to assess its future performance. The milliQan experiment has since been approved and is currently undergoing construction.