Older sewer lines are made of clay and joined together. Tree and bush roots in their never ending search for water will invade the pipes in search of water and eventually break into your sewer drain line. Action should be taken immediately. If you allow your drain line to become overrun by tree/bush roots, you will inevitably end up replacing your sewer line which is very costly and requires digging up your entire yard. The digging may even require the removal of the tree creating the issue; maintenance to your sewer line can prevent the problem from becoming a costly issue.
The best way to prevent this from happening is an period drain rodding. The drain rodding will cut the tree roots forcing them back for some time. This maintenance should occur on a semi-annual or annual basis.
See the illustration below for an example of roots destroying your sewer line.