In this review, we consider a general theoretical framework for fermionic color-singlet states, including a singlet, a doublet and a triplet under the standard model SU(2)$_{\rm L}$ gauge symmetry, corresponding to the Bino, Higgsino and Wino in Supersymmetric theories, generically dubbed as "electroweakinos" for their mass eigenstates. Depending on the relations among their three mass parameters and the mixings after the electroweak symmetry breaking, this sector leads to rich phenomenology potentially accessible at the current and near-future experiments. We discuss the decay patterns of the electroweakinos and their observable signatures at colliders. We review the existing bounds on the model parameters. We summarize the current status for the comprehensive searches from the ATLAS and CMS experiments at the LHC. We comment on the prospects for future colliders. An important feature of the theory is that the lightest neutral electroweakino can be identified as a WIMP cold dark matter candidate. We take into account the existing bounds on the parameters from the dark matter direct detection experiments and discuss the complementarity for the electroweakino searches at colliders.
Comment: 33 pages, 13 figures. Invited review prepared for publication in the Annual Review of Nuclear and Particle Science, Volume 70 (2020)