The goal of this thesis was to research and analyze the literature that deals with quantum aspects of black hole entropy, with a heavy emphasis on quantum corrections. In the first chapter, we generalize ’Hooft’s brick wall method to higher-dimensional black holes, and we apply those results to the Schwarzschild and Reissner-Nordström black holes. In the second chapter, we look at the entanglement between the degrees of freedom inside and outside a black hole, while considering the horizon as the entanglement surface and interpreting the obtained entropy as the entropy of the black hole. We present two methods that simplify the calculations of the entanglement entropy: the replica trick, where we turn the task of calculating the entanglement entropy to calculating the partition function on a replicated manifold, and the heat kernel method, where we calculate the entropy by taking the trace of the so-called heat kernel. In the third chapter, we consider the one-loop renormalization of the gravitational action, and using the Pauli-Villars regulator, we show that it leads to the renormalization of the Bekenstein-Hawking entropy. In the final chapter, we conclude with a discussion on the applicability of these methods to lower-dimensional black holes.