For regular grime and stains, put the racks in the sink and wet them with water before adding a drop of dish soap. Then, crumple foil into a ball and wet it with water, too.
If the rack is really grimy, cover it in aluminum foil, soak it entirely in hot water in a bathtub while laying it on a towel to protect the tub, and then place a dishwasher pod.
The foil will chemically react with the pod, loosening the grease and buildup. After a few hours, remove the foil, ball it up, and use it to slough off all the grease and debris.