Compound events (CEs) are weather and climate events that result from multiple hazards or drivers with the potential to cause severe socio-economic impacts. Compared with isolated hazards, the multiple hazards/drivers associated with CEs can lead to higher economic losses and death tolls. Here, we provide the first analysis of multiple multivariate CEs potentially causing high-impact floods, droughts, and fires. Using observations and reanalysis data during 1980-2014, we analyse 27 hazard pairs and provide the first spatial estimates of their occurrences on the global scale. We identify hotspots of multivariate CEs including many socio-economically important regions such as North America, Russia and western Europe. We analyse the relative importance of different multivariate CEs in six continental regions to highlight CEs posing the highest risk. Our results provide initial guidance to assess the regional risk of CE events and an observationally-based dataset to aid evaluation of climate models for simulating multivariate CEs.