Sitting at the heart of nearly all galaxies is a massive black hole, that, while typically 1000 times less massive than the galaxy in which it resides, has the potential to release enough energy via accretion of gas onto the black hole, to completely unbind the entire galaxy. Most of the power from an Active Galactic Nucleus (AGN) is released close to the black hole, and thus studying the inner accretion flow, at the intersection of gas inflow and energy outflow, is essential for understanding how black holes grow and affect galactic evolution. In the past decade, we have had a breakthrough in how we probe the inner accretion flow, through the discovery of X-ray Reverberation Mapping, where X-rays produced close to the black hole reverberate off inflowing gas. By measuring reverberation time delays, we can quantify the effects of strongly curved space time and the black hole spin, which is key for understanding how efficiently energy can be tapped from the accretion process. In this talk, I will give an overview of this field, and show how extending these X-ray spectral-timing techniques to transient accretion episodes is helping us probe the formation of X-ray coronae, jets and other relativistic outflows.