This study aims to review the early history of dark matter study, such as observational evidence from galactic rotational curves, gravitational lensing, and the cosmic microwave background, among others. The observation of the bullet clusters, which strongly supports the existence of dark matter rather than the theory of modified gravity, is discussed. The N body simulations also suggest the existence of cold non-relativistic dark matter and the existence of a universal form of the dark matter density distribution profile. We introduce a standard mechanism of thermal freeze-out for dark matter relic abundance, i.e., an explanation of how the dark matter particles that were kept in thermal equilibrium in the early stages of the universe are later unable to stay in equilibrium due to the expansion of the universe. The typical dark matter candidates are the so-called WIMPs (weakly interacting massive particles). Popular WIMP candidates include the lightest supersymmetric particles such as neutralinos. Other WIMP candidates such as the lightest T odd particles in the little Higgs models and the lightest KK (Kluza-Klein) modes in the universal extra dimension models are also discussed. Non-WIMP dark matter candidates such as axions are briefly discussed. The basic ideas and methods of dark matter detection, such as underground direct detection, which involves dark matter scattering off target nuclei, and indirect detection in space, which involves dark matter annihilation or decay in galaxies, are reviewed with a focus on recent experimental developments. For underground direct detection, we begin with the basic formulas for elastic dark matter nuclei scattering and the general features of nuclear number dependence. Three types of observables are discussed: (1) direct recoil events, (2) solar modulation of the recoil events, and (3) directional effects or the day-night differences of the events. Then, we focus on the experiments studying low-mass dark matter below 10 GeV, such as SuperCDMS (super cryogenic dark matter search) and CDEX (China dark matter experiment), among others, with a special focus on the CDEX experiment, which uses point contact germanium detectors. Experiments studying high-mass dark matter using liquid argon, such as Xenon, PandaX (particle and astrophysical xenon detector), and DarkSide are also discussed. Directional detection experiments, such as DRIFT (directional recoil identification from tracks) and MIMAC (MIcro-tpc MAtrix of Chambers), are briefly discussed. For indirect detection experiments in space, we first introduce the basic theory of dark matter signals in cosmic rays and then discuss the importance of the propagation effects of high-energy cosmic rays, such as electrons, positrons, protons, antiprotons, and heavier cosmic ray nuclei. The uncertainties originating from various sources are also discussed. We then review recent experimental results, such as that from Fermi LAT (Fermi large area telescope) and AMS-02(Alpha magnetic spectrometer 02), with a focus on the most recent dark matter particle explorer (DAMPE) experiments. As nearby sources may contribute to CRE (cosmic ray electron) structures at high energies, the recently released DAMPE results on the CRE flux, which hinted at a narrow excess at energy of 1.4 TeV, is discussed in some detail. In general, a spectral structure with a narrow width appears to reveal the space time distribution of the sources. Future perspectives of heavier cosmic-ray nuclei, such as anti-deuteron and anti-helium, are also reviewed.
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