Ha, I actually dealt with this today.
After looking around I found that missing textures can be caused by a number of things, one of them is the Alpha slider at the bottom of your Shader node is set to 0 which can sometimes result in the textures not appearing. The other possible cause is the setting when importing or exporting an fbx file. When importing make sure that image search is ticked as if you're using an image texture the computer will need a filepath to find it (if ur object is bright pink that's probably what happened). When exporting, check the top of the side bar to find the different settings for file paths when exporting, when you're sending to someone who doesn't have the images saved locally, a little box next to the "Path Mode" drop-down will let you imbed textures you would otherwise need locally. If you didn't make the textures try contacting whoever made the model to see if they can send you any missing image textures. If all else fails you may have to straight copy the texture information in the nodes(if you have them of course).
Finally, it sounds dumb but it's happened to me before, check that your viewport is set to render textures, it can be very easy to forget which one ur on & panic.
- Good Luck