The interplay of sunlight with clouds is a ubiquitous and often pleasant visual experience, but it conjures up major challenges for weather, climate, environmental science, and beyond. Those engaged in the characterization of clouds (and the clear air nearby) by remote sensing methods are possibly even more confronted. The problem comes, on the one hand, from the spatial complexity of real clouds and, on the other hand, from the dominance of multiple scattering of light. The former ingredient contrasts sharply with the still popular representation of clouds as homogeneous plane-parallel
slabs for the purposes of radiative transfer. In typical cloud scenes, the
opposite asymptotic transport regimes of diffusion and ballistic propagation coexist. At sufficiently high altitudes and/or latitudes, the problem is compounded by the occurrence of a myriad shapes of ice crystals. We survey the three-dimensional atmospheric radiative transfer literature over the past fifty years and identify at present three intertwining thrusts. How to assess the damage (bias) caused by 3D effects in
the operational 1D radiative transfer models? How to mitigate this damage? Can
we exploit 3D radiative transfer phenomena to innovate observation methods and technologies? We quickly realize that the smallest scale resolved computationally or observationally may be artificial but is nonetheless a key quantity that separates the 3D radiative transfer solutions into two broad and complementary classes: stochastic and
deterministic. Both approaches draw on classic and modern statistical, mathematical and computational physics.