There are many reasons a dog may destroy your belongings. For example, puppies that are not supervised will explore anything. If it smells good, tastes good or feels good they will play with it. By play, I mean chase it, kill it and eat it. If no one is nearby to say, "Stop that", the behavior continues. 

Destructive behavior can also be attention seeking behavior. If running around with your shoe causes you to drop whatever you are doing to chase the dog, then your dog is using the destructive behavior to get your attention. He may benefit from a vigorous exercise program or positive attention from you for desirable behavior. Actively reward a dog with attention for playing quietly every chance you get. Your dog may also benefit from a leadership training program to teach him that all things in the house belong to you. 

Another cause for destructive behavior is a desire to reach something outside the house or room or fence he is confined to. If the destructive behavior is centered around doorways, windows or fences, your dog may have a problem with territorial or predatory aggression and may be reacting to a trespasser such as the mail carrier or a neighbor's cat. I have observed squirrels park on an outside window and work a dog inside a house into a frenzy. This barrier frustration usually usually occurs whether you are home or not.

Finally, some dogs panic when left alone. These dogs are not destructive when supervised and are house trained. But when left alone, even for just 30 minutes, they wreak havoc in the house. These dogs can be suffering from Separation Anxiety. This is a specific form of destruction related to insecurity which can be handled with separation training.