River flows change on timescales ranging from minutes to millennia. These variations influence fundamental functions of ecosystems, including biogeochemical fluxes, aquatic habitat, and human society. Efforts to describe temporal variation in river flow—i.e., flow regime—have resulted in hundreds of unique descriptors, complicating interpretation and identification of global drivers of flow dynamics. Here, we used a cross-disciplinary analytical approach to investigate two related questions: 1. Is there a low-dimensional structure that can be used to simplify descriptions of streamflow regime? 2. What catchment characteristics are most associated with that structure? Using a global database of daily river discharge from 1988-2016 for 3,120 stations, we calculated 189 traditional flow metrics, which we compared to the results of a wavelet analysis. Both quantification techniques independently revealed that streamflow data contain substantial low-dimensional structure that correlates closely with a small number of catchment characteristics. This structure provides a framework for understanding fundamental controls of river flow variability across multiple timescales. Climate was the most important variable across all timescales, especially those lasting several weeks, and likely contributes as much as dams in controlling flow regime. Catchment area was critical for timescales lasting several days, as was human impact for timescales lasting several years. In addition, both methods suggested that streamflow data also contain high-dimensional structure that is harder to predict from a small number of catchment characteristics (i.e. is dependent on land use, soil structure, etc.), and which accounts for the difficulty of producing simple hydrological models that generalize well.