A global database of large explosive volcanic eruptions has been compiled for the Holocene and analyzed using extreme value theory to estimate magnitude-frequency relationships. The database consists of explosive eruptions with magnitude (M) greater than or equal to 4. Two models are applied to the data, one assuming no underreporting of eruptions and the other taking underreporting into consideration. Results from the latter indicate that the level of underreporting is high and fairly constant from the start of the Holocene until about 1 A. D. and then decreases dramatically toward the present. Results indicate there is only a similar to 20% probability that an explosive eruption of M = 6 occurring prior to 1 A. D. is recorded. Analysis of the data set in the time periods 1750 A. D. and 1900 A. D. to present (assuming no underreporting) suggests that that these periods are likely to be too short to give reliable estimates of return periods for explosive eruptions with M > 6. Analysis of the Holocene data set with corrections for underreporting bias provide robust magnitude-frequency relationships up to M = 7. Extrapolation of the model to greater magnitudes (M > 8) gives results inconsistent with geological data, predicting eruption size upper limits much smaller than known eruptions such as the Fish Canyon Tuff. We interpret this result as the consequence of different mechanisms operating for explosive eruptions with M > 7.