First, make sure that you have symbolized any data you want preserved and added a legend. This allows you to identify the values associated with each color later. Don’t worry if some of your colors are very similar; you can use Color Match to individually identify them in Illustrator.
You are now ready to export to Illustrator.

When you open the file in Illustrator later, a warning message will pop up. Be sure to select Update (not OK) or the legend text will disappear.
Files saved as PDFs maintain the same layers as .ai files, but all layers are under clipping masks. Click Object > Clipping mask > Release several times to release objects.
Note that exporting to Illustrator preserves vector layers, but only keeps what is on top of the image. To view layers separately, save the file as a PDF by repeating step 1 but selecting 'PDF' instead of 'AI' for 'Save as Type'.