Some cats may not have any signs of dental disease. This makes regular (at least annual) veterinary checkups important. Not only will the vet examine your cat's body, but they will also check their teeth and gums.
Signs of gum disease in cats often include the symptoms you may see in a human - redness, swelling, and bleeding. While your cat can't tell you they're in pain, discomfort is also a sign of gingivitis or periodontitis. But your cat may not act like themselves or may not eat/have trouble eating.
Tooth resorption may also make eating painful for your cat. Along with eating issues, this type of dental disease can also cause discoloration or loss of the tooth. A pinkish area at the bottom of the tooth (where it meets the gums) is a late sign of this condition.