To find out why your cat chews on things, you must first observe his/her behavior when they chew. If it's when their food dish is empty, hunger is a driving force. If your cat gets frisky and begins chewing on things, then perhaps he or she is bored and needs some attention. If the chewing occurs when another animal enters the room or when you have company, then the chewing is likely related to nerves or insecurity (think of a child sucking their thumb when they are nervous).
Once you know why your cat is chewing on things, it's easier to distract their attention to something else. Before long, with a bit of chew toys, love, and food when they are hungry, your cat will stop chewing on the things in your house.
note: bitter apple spray applied to cords and shoes help to curb this behavior too, especially when what they are chewing on is potentially dangerous.