Weakly Interacting Massive Particles (WIMPs) are among the best-motivated dark matter candidates. No conclusive signal, despite an extensive search program that combines, often in a complementary way, direct, indirect, and collider probes, has been detected so far. This situation might change in near future due to the advent of one/multi-TON Direct Detection experiments. We thus, find it timely to provide a review of the WIMP paradigm with focus on a few models which can be probed at best by these facilities. Collider and Indirect Detection, nevertheless, will not be neglected when they represent a complementary probe.

Designed as a high-sensitivity gamma-ray observatory, the Fermi Large Area Telescope is also an electron detector with a large acceptance exceeding $2{\mathrm{m}}^2\mathrm{sr}$ at 300 GeV. Building on the gamma-ray analysis, we have developed an efficient electron detection strategy which provides sufficient background rejection for measurement of the steeply falling electron spectrum up to 1 TeV. Our high precision data show that the electron spectrum falls with energy as $E^{-3.0}$ and does not exhibit prominent spectral features. Interpretations in terms of a conventional diffusive model as well as a potential local extra component are briefly discussed.

Satellite galaxies of the Milky Way are among the most promising targets for dark matter searches in gamma rays. We present a search for dark matter consisting of weakly interacting massive particles, applying a joint likelihood analysis to 10 satellite galaxies with 24 months of data of the Fermi Large Area Telescope. No dark matter signal is detected. Including the uncertainty in the dark matter distribution, robust upper limits are placed on dark matter annihilation cross sections. The $95\%$ confidence level upper limits range from about ${10}^{-26}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ at 5 GeV to about $5\times {10}^{-23}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ at 1 TeV, depending on the dark matter annihilation final state. For the first time, using gamma rays, we are able to rule out models with the most generic cross section ($\sim 3\times {10}^{-26}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ for a purely $s$-wave cross section), without assuming additional boost factors.

We update the phenomenology of gauge-singlet extensions of the Standard Model scalar sector and their implications for the electroweak phase transition. Considering the introduction of one real scalar singlet to the scalar potential, we analyze present constraints on the potential parameters from Higgs coupling measurements at the Large Hadron Collider (LHC) and electroweak precision observables for the kinematic regime in which no new scalar decay modes arise. We then show how future precision measurements of Higgs boson signal strengths and the Higgs self-coupling could probe the scalar potential parameter space associated with a strong first-order electroweak phase transition. We illustrate using benchmark precision for several future collider options, including the high-luminosity LHC, the International Linear Collider, Triple-Large Electron-Positron collider, the China Electron-Positron Collider, and a 100 TeV proton-proton collider, such as the Very High Energy LHC or the Super Proton-Proton Collider. For the regions of parameter space leading to a strong first-order electroweak phase transition, we find that there exists considerable potential for observable deviations from purely Standard Model Higgs properties at these prospective future colliders.