Estimating the spatial distribution of snow water equivalent (SWE) in mountainous terrain is currently the most important unsolved problem in snow hydrology. Several methods can estimate the amount of snow throughout a mountain range: (1) Spatial interpolation from surface sensors constrained by remotely sensed snow extent provides a consistent answer, with uncertainty related to extrapolation to unrepresented locations. (2) The remotely sensed date of disappearance of snow is combined with a melt calculation to reconstruct the SWE back to the last significant snowfall. (3) Passive microwave sensors offer real-time global SWE estimates but suffer from several problems like subpixel variability in the mountains. (4) A numerical model combined with assimilated surface observations produces SWE at 1-km resolution at continental scales, but depends heavily on a surface network. (5) New methods continue to be explored, for example, airborne LiDAR altimetry provides direct measurements of snow depth, which are combined with modelled snow density to estimate SWE. While the problem is aggressively addressed, the right answer remains elusive. Good characterization of the snow is necessary to make informed choices about water resources and adaptation to climate change and variability.