In this thesis, we present various results concerning the structure of matter close to black holes when they are actively accreting. The two components (apart from the black hole itself) most relevant to this work are the accretion disc and X-ray emitting corona. We use various methods to help determine their location, properties and relation to each other.

In chapters 2 and 3, we consider how thermal emission from the accretion disc is affected by the coronal emission. Chapter 2 presents an analysis of a sample of supermassive black hole (SMBH) sources, showing that in many of these sources, variability in the accretion disc emission is driven by heating from the central source. Chapter 3 presents results from a dedicated campaign on a particularly X-ray variable object, IRAS 13324-3809, which however does not show disc variability in response to X-ray variations. We discuss potential reasons for this.

Chapters 4 and 5 consider what we can learn about accreting black holes from their X-ray spectra. Chapter 4 describes the use of X-rays which reflect from the disc to study properties of the disc such as its innermost extent (governed in part by the black hole spin) and ionisation state. Chapter 5 analyses hard X-ray spectra of two sources, including the electron temperature of the corona, and considers the physical process which could produce the observed temperature.

Finally, in chapter 6, we use a number of the techniques utilised previously to perform an in-depth study of the recent outburst from the stellar-remnant black hole in the MAXI 1820+070 X-ray binary system in our own Galaxy. As they are much smaller, such systems can show far more drastic state changes on observable timescales than SMBH can; the reasons for these state changes are not yet fully explained. The reflected emission shows that the disc extends close to the black hole, which has not been universally accepted in the state observed here. That the reflecting disc extends so close to the black hole also constrains the possible causes of characteristic timescales (QPOs) in the variability.