We put in a new range hood filter in January. The filter easily slides out and can go in the dishwasher. What could be easier?

If they won't fit in your dishwasher you can use something as simple as Dawn dishwashing detergent. Fill a sink using hot water/detergent and find something to weight the filter so it doesn't float. Let set and come back and rinse.

I have also used a product called Oil Eaters that works great for not only grease but brake dust off of expensive car wheels, super grimy bbq's, and even spray it on my paint brushes before I start cleaning them with soap. As with any product read the instructions and test before using.