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Cosmic shear galaxy surveys are now achieving high precision in their measurements of cosmological parameters that describe the dark sector of our Universe, competing with the precision of CMB experiments such as Planck. In this presentation, I will explain how cosmic shear data is analysed, starting from lensing galaxy catalogues to constraints on dark matter and dark energy. In particular, I will present a powerful analysis technique based on peak count statistics, as measured recently from the Kilo Degree Survey and the Dark Energy Survey, and discuss some of the potential and challenges we will face when analysing the upcoming generation of data from LSST and Euclid.