Upcoming weak lensing surveys such as Rubin and Euclid are designed to improve by an order of magnitude the precision on the so-called Dark Sector of the Universe. The early forecasts upon which accuracy targets were set all assumed that cosmology would be mostly learned from measurements of the shear two-point functions. Although this choice was well motivated from a theoretical point of view, new developments in the field have revealed that alternative methods can significantly outperform the original plan. In this talk I will introduce some of the current efforts in “Beyond-two point Statistics”, show why these new methods do much better at constraining dark matter and dark energy, and present a roadmap to prepare their use for upcoming surveys.