The cosmological standard model, which describes the accelerated expansion of the Universe, is well established. However, several lingering issues remain, including the nature of Dark Energy and tensions between measurements in the early and local Universe. One tool to address these questions is the weak gravitational lensing effect, which describes the distortion of observed galaxy shapes by the matter distribution of the Universe.

In this talk, I will give an overview of weak lensing is used to determine cosmological parameters, as well as some of the challenges of these analyses. The power of weak lensing analyses can be considerably improved by using new types of statistics called higher-order statistics (HOS). I will introduce one particular HOS, the third-order shear statistic, which is a promising method for better understanding the structure of the Universe. Finally, I will present the next step for weak lensing analyses - the Euclid telescope, which will be launched later this year.