My research focuses on accreting compact objects, mainly stellar-mass black holes accreting gas from their binary partner in a so-called X-ray binary system, but I am also interested in accreting neutron stars and active galactic nuclei. I analyse and model X-ray observations of these systems in order to learn about the very strong gravitational field present close to the event horizon. In particular, I develop and use sophisticated techniques that exploit the rapid stochastic variability seen in the X-ray signal in order to map the accretion flow in the immediate vicinity of the black hole. This includes using Doppler shifts to detect a wobble of the inner accretion flow predicted by General Relativity known as Lense-Thirring precession, modelling aperiodic X-ray variability as inward propagating fluctuations of the density of the accretion disk, and using light crossing delays for the purposes of reverberation mapping.