String theory provides with a consistent framework which combines quantum mechanics and gravity. Two grand challenges of fundamental physics - building realistic models of black holes and cosmologies - can be addressed in this framework thanks to novel holographic methods.Recent astrophysical evidence indicates that some black holes rotate extremely fast, as close as 98% to the extremality bound. No quantum gravity model for such black holes has been formulated so far. My first objective is building the first model in string theory of an extremal black hole. Taking on this challenge is made possible thanks to recent advances in a remarkable duality known as the gauge/gravity correspondence. If successful, this program will pave the way to a description of quantum gravity effects that have been conjectured to occur close to the horizon of very fast rotating black holes.Supernovae detection has established that our universe is starting a phase of accelerated expansion. This brings a pressing need to better understand still enigmatic features of de Sitter spacetime that models our universe at late times. My second objective is to derive new universal properties of the cosmological horizon of de Sitter spacetime using tools inspired from the gauge/gravity correspondence. These results will contribute to understand its remarkable entropy, which, according to the standard model of cosmology, bounds the entropy of our observable universe.