At the dawn of precision Cosmology, accurate control of systematic errors and efficient combination and exploration of complementary cosmological probes across surveys has become increasingly important. A dominant source of systematic error in cosmological data are uncertainties in the distance, or redshift, of galaxies. The `redshift' of galaxies parametrizes how the wavelength of light is `stretched' under an expanding background universe, and can be seen both as a measure of galaxy distance, and time. Thus, describing the galaxy positions as a Spatio-temporal point process, a fundamental challenge is to perform inference under uncertain, or latent, redshift measurements. I will describe both the physical and statistical relevance of this problem, focussing on problems of regularization, identifiability, likelihood construction, and scalability.