Measurements of the large-scale structure of the universe are key observables to study fundamental physics. This thesis focuses on the calibration of photometric redshift distributions of extragalactic galaxy surveys and their impact on the analysis of large-scale structure data.

First, I examine the impact of redshift distribution uncertainties on the cosmological inference from weak lensing measurements. The weak gravitational lensing effect, known as cosmic shear, distorts the shape of galaxy images due to the distribution of gravitating matter along the line sight. Thus, it provides a probe of the matter distribution in the universe. However, modelling the observed cosmic shear signal requires knowledge about the distribution of observed galaxies along the line of sight, which is usually determined through photometric redshifts. I develop a method that accurately propagates residual redshift distribution uncertainties into the weak lensing likelihood and perform a self-calibration of the redshift distribution with cosmic shear data.

Second, I develop a new method to assign photometrically observed galaxies to tomographic redshift bins. The goal is to obtain compact distributions and to reduce the overlap between redshift bins caused by catastrophic outliers in the photometric redshift estimation. This is achieved by combining a self-organising map with a simulated annealing algorithm which optimises the clustering cross-correlation signal between a photometric galaxy catalogue and a spectroscopically observed sample of reference galaxies.

Finally, I perform consistency tests in cosmological analyses. These tests include a study of the consistency between the constraints on cosmological parameters probed by the five tomographic bins of the Kilo-Degree Survey. Furthermore, I study the internal consistency of the ΛCDM model by dividing the model into regimes: one that describes the evolution of the isotropic background of the universe and one describing matter density perturbations. This model is constrained by cosmic shear, galaxy clustering, and cosmic microwave background measurements.