OpenEXR is the advanced floating point image format created at Industrial
Light and Magic and the best format to use when working with 32-bit HDR
imagery in Photoshop and After Effects. However, Adobe's support for the
format is minimal - only with ProEXR can digital artists finally access all
the power available in OpenEXR.

OpenEXR can support multiple layers of imagery, but Photoshop can't read or
save layered EXR files...unless you have ProEXR. Store all your layers in
one file and read them into After Effects, Nuke, Shake, and Fusion. Or in
one step save layers as individual files for programs that are less EXR
savvy. ProEXR will also read all the image buffers created by modern 3D
renderers and place each in its own Photoshop layer.

ProEXR lets you choose from all the compression options available in
OpenEXR. Most EXR compression is lossless, but one of the most interesting
options is a lossy method similar to JPEG, applied to the world of floating
point. Using B44 compression and Luminance/Chroma sampling, HDR images can
be crushed to a fraction of their uncompressed size, usually without visible
artifacts, only in ProEXR.