This chapter starts with a general description of extreme events characterised by heavy tailed distributions with a few very large values compared to the other values of the data set. Typical examples of power law scaling are the Gutenberg and Richter magnitude frequency relation and the Omori law for aftershock decay. However, both are open-ended distributions and therefore have no characteristic scale, i.e. there is no upper limit on magnitude in the former and there is no end to the duration of aftershock sequences in the latter. Therefore, a need arises for a more physical description, by introducing either a soft transition to finite energy release or a sharp cut-off by a double-truncated distribution. Another important issue described in this chapter is the so -called \(m_{max}\) or log \(P_{max}\) , which in earthquake seismology is the maximum magnitude, or potency, earthquake that a given seismogenic region can deliver. However, in mines the maximum possible size event scales with the footprint of the mine and with the degradation of rock mass stiffness, both increasing as mining progresses creating conditions conducive for ever larger events to occur. Therefore, the maximum size event associated with mining is not an ultimate number but needs Mendecki (March 11, 2025)—Elements of Seismic Hazard in Mines, Springer Preface 2 to be estimated periodically. It is the next record breaking seismic potency, energy, or magnitude which can be estimated and that needs to be managed.