Gamma-Ray Dark Matter Searches in Milky Way Satellites -- A Comparative Review of Data Analysis Methods and Current Results

If dark matter is composed of weakly interacting particles with mass in the GeV-TeV range, their annihilation or decay may produce gamma rays that could be detected by gamma-ray telescopes. Observations of dwarf spheroidal satellite galaxies of the Milky Way (dSphs) benefit from the relatively accurate predictions of dSph dark matter content to produce robust constraints to the dark matter properties. The sensitivity of these observations for the search for dark matter signals can be optimized thanks to the use of advanced statistical techniques able to exploit the spectral and morphological peculiarities of the expected signal. In this paper, I review the status of the dark matter searches from observations of dSphs with the current generation of gamma-ray telescopes: Fermi-LAT, H.E.S.S, MAGIC, VERITAS and HAWC. I will describe in detail the general statistical analysis framework used by these instruments, putting in context the most recent experimental results and pointing out the most relevant differences among the different particular implementations. This~will facilitate the comparison of the current and future results, as well as their eventual integration in a multi-instrument and multi-target dark matter search.