Throughout the past decade, the Gravity Recovery and Climate Experiment (GRACE) has given an unprecedented view on global variations in terrestrial water storage. While an increasing number of case studies have provided a rich overview on regional analyses, a global assessment on the dominant features of GRACE variability is still lacking. To address this, we survey key features of temporal variability in the GRACE record by decomposing gridded time series of monthly equivalent water height into linear trends, inter-annual, seasonal, and subseasonal (intra-annual) components. We provide an overview of the relative importance and spatial distribution of these components globally. A correlation analysis with precipitation and temperature reveals that both the inter-annual and subseasonal anomalies are tightly related to fluctuations in the atmospheric forcing. As a novelty, we show that for large regions of the world high-frequency anomalies in the monthly GRACE signal, which have been partly interpreted as noise, can be statistically reconstructed from daily precipitation once an adequate averaging filter is applied. This filter integrates the temporally decaying contribution of precipitation to the storage changes in any given month, including earlier precipitation. Finally, we also survey extreme dry anomalies in the GRACE record and relate them to documented drought events. This global assessment sets regional studies in a broader context and reveals phenomena that had not been documented so far.