DES+KiDS: Cosmic shear cosmology with 127 million galaxies

Cosmic shear galaxy surveys are now achieving precision of a few percent in their measurements of cosmological parameters that describe the dark sector of our Universe, comparable with CMB experiments such as Planck. While most analyses are based on volume-averaged methods, it has become clear that much better results can be achieved  when harnessing the richness of the full cosmic web. In this talk, I will review the basics of cosmic shear data analyses, starting from lensing galaxy catalogues to constraints on dark matter and dark energy. I will then present a powerful technique based on peak count statistics, as measured recently from the Kilo Degree Survey and the Dark Energy Survey, providing the tightest cosmic shear measurement to date. I will draw lessons from this and discuss some of the key challenges we will face with the upcoming generation of data from LSST and Euclid.