If they are only slightly dirty, warm soapy water with Dawn dish soap will do it. If they are very dirty, like we have found in rentals, we use a degreaser meant for autos. This may sound crazy, but it works and will not harm the cabinets. I will share a photo of the product. Wipe it in a small area ( 6 inch by 6 inch for example) and let it soak for ten minutes or so. Then use an old tooth brush to scrub it. Wipe it clean with a damp rag and reapply as needed. It works best on the doors to remove them one at a time to clean.
TSP, Krud Kutter.
Dawn platinum light rag with warm water, put on let sit and wipe off 5 min later
OrangeGlo for light cleaning
A paste of baking soda & hydrogen peroxide apply with a scrub brush for medium build up
Kitchen and wood safe degreaser like GP66 or Fuller’s for heavy build up