Weak lensing cosmological constraints through the measurement of spatial correlation of galaxy shape (cosmic shear) is known to be one of the most potent cosmic probes to test General Relativity with an optical wide-field survey such as the Vera Rubin Observatory (LSST). However, measuring the cosmic shear is challenging due to different systematic effects on galaxy shape measurement. As galaxy shape measurement is the starting point of a cosmological analysis using weak lensing, having a biased estimation of galaxy shape will bias cosmological measurement. In this talk, I will review what we mean when we speak of doing a cosmological analysis using weak lensing, the different challenges of extracting the cosmic shear signal, and present some of my work that I did since I left the LPC on that topic.