The X-ray spectrum of many accreting black holes can be modelled as due to a direct power-law continuum and a reflected spectrum, produced by irradiation of the accretion disc by the continuum. Spectral features in the reflection spectrum enable us to model the geometry of the emitting and reflecting regions and, in particular, estimate the spin of the black hole. Variations in the continuum should be see in the reflection after a time delay, or lag, due to the increased light path taken. Depending on mass, lags range from less than a minute to tens of minutes for the innermost regions of a Seyfert galaxy. We first detected such lags about 4 years ago and they have now been seen in more than a dozen AGN. Studies of the reverberation process confirm the reflection picture and are enabling us to map out the environment of the accretion flow immediately around the black hole.