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Recently data from PAMELA, ATIC, FERMI-LAT and HESS show that there are$e^{\pm}$ excesses in the cosmic ray energy spectrum. PAMELA observed excessesonly in $e^+$, but not in anti-proton spectrum. ATIC, FERMI-LAT and HESSobserved excesses in $e^++e^-$ spectrum, but the detailed shapes are differentwhich requires future experimental observations to pin down the correct dataset. Nevertheless a lot of efforts have been made to explain the observed$e^\pm$ excesses, and also why PAMELA only observed excesses in $e^+$ but notin anti-proton. In this brief review we discuss one of the most popularmechanisms to explain the data, the dark matter annihilation. It has long beenknown that about 23% of our universe is made of relic dark matter. If the relicdark matter was thermally produced, the annihilation rate is constrainedresulting in the need of a large boost factor to explain the data. We willdiscuss in detail how a large boost factor can be obtained by the Sommerfeldand Briet-Wigner enhancement mechanisms. Some implications for particle physicsmodel buildings will also be discussed.

A Brief Review on Dark Matter Annihilation Explanation for $e^\pm$ Excesses in Cosmic Ray