Struggles of Anaerobic Digestion

I'm doing a bit of research about treatment chains as well as trying to understand a bit more about the effluents from AD and Biogas. 

Firstly, what industries are these systems mostly used in and, if any, what is used as a post-treatment for the water?

I'm aware that they can typically reduce COD to around 500ppm, depending on the application, but for people out there with experience what sort of chemicals/pollutants/colour does this process struggle to deal with?

What is being left in there that may stop you from reaching your discharge consent's or force you to look down further avenues for treatment?

Thanks for any help.