Atmospheric circulation patterns derived from multi-spectral remote sensing can serve as a guide for choosing a suitable entry site for a future in situ probe mission. Since the Voyager-2 flybys in the 1980s, three decades of observations from ground- and space-based observatories have generated a picture of Ice Giant circulation that is complex, perplexing, and altogether unlike that seen on the Gas Giants. This review seeks to reconcile the various competing circulation patterns from an observational perspective, accounting for spatially-resolved measurements of: zonal albedo contrasts and banded appearances; cloud-tracked zonal winds; temperature and para-H$_2$ measurements above the condensate clouds; and equator-to-pole contrasts in condensable volatiles (methane and hydrogen sulphide) in the deeper troposphere. These observations identify three distinct latitude domains: an equatorial domain of deep upwelling and upper-tropospheric subsidence, potentially bounded by peaks in the retrograde zonal jet and analogous to Jovian cyclonic belts; a mid-latitude transitional domain of upper-tropospheric upwelling, vigorous cloud activity, analogous to Jovian anticyclonic zones; and a polar domain of strong subsidence, volatile depletion, and small-scale (and potentially seasonally-variable) convective activity. Taken together, the multi-wavelength observations suggest a tiered structure of stacked circulation cells (at least two in the troposphere and one in the stratosphere), potentially separated in the vertical by (i) strong molecular weight gradients associated with cloud condensation, and by (ii) transitions from a thermally-direct circulation regime at depth to a wave-driven circulation regime at high altitude. The inferred circulation can be tested in the coming decade by 3D simulations and by observations from future world-class facilities. [Abridged]