One of our rentals have termite infestation three years ago. We noticed because parts of the walls behind picture frames are being eating. Tracks all over the place. We called a few company to help with termites treatment. They're very expensive. But if it's your house, you don't want to take a chance of it falling down on your head. This site discusses issues with termites.
There was also a house we bought with termites infestation but the seller didn't tell this. I could have use website like this which tells me how to do a termite inspection so I could tell for myself. I could have save myself a lot of trouble, or at the very least, save myself money. Information is power, so if you want to know about termites, click on one of the links on this post.