A key element in the assessment of seismic hazard is estimation of the maximum possible earthquake magnitude, Mmax. A great deal of effort has been invested in developing approaches to estimate Mmax for natural (tectonic) earthquakes, especially in regions of relatively low seismicity where it is difficult to associate observed seismicity with known geological faults. In probabilistic seismic hazard analysis, there has been a tendency to assign a narrow range of large values to Mmax. This results in the impression that hazard results are insensitive to this parameter, which is not the case when the Mmax distribution captures the full range of possible values. For induced seismicity, Mmax estimates can have far-reaching implications both in terms of quantitative assessments of the resulting seismic hazard and risk, and in terms of the public and regulatory perception of this risk. Estimates of Mmax for induced seismicity need to distinguish between driven earthquakes, for which magnitudes are largely controlled by operational parameters, and triggered tectonic earthquakes, together with estimates of the likelihood of such triggering. Distributions of triggered Mmax may be limited to smaller magnitudes than distributions for natural seismicity due to the shallow depth of most injection/extraction wells. For the management of induced seismic risk, the expected largest event magnitude (which may be influenced by a Traffic Light Scheme in operation) may be more relevant than any physical upper bound truncating the recurrence relationship.