One of the best ways to handle backbiters is to simply ignore them. The very fact that they are saying bad things about you behind your back goes to prove that they do not respect you very much and therefore feel no shame in gossiping about you or being jealous of you. While gossip is a form of social entertainment that goes bigger and uglier with the passage of time, jealousy is something that is strong since the very first day. Someone may be finding it extremely hard to digest your success and therefore takes out his frustration by targeting your reputation. Since both the gossipers and jealous people do not respect you, it is best to ignore them. Do not give them the satisfaction by showing any signs of distress or anger.
If the backbiting is making an impact on your personal or professional life, it is extremely important for you to put a stop to it. Identify the person who is slandering you and confront him. Ask him why they are saying bad things about you behind your back. Keep your cool as it will encourage them to talk. Once you hear about the problem, sort it out in a civilised manner. You may have done something in the past to hurt that person and therefore he may be simply taking revenge. Sort out the issue and return to a slander-free life.
You can make the slandering stop by letting the backbiter know that you know what they are up to and show through your actions that you have forgiven them. Extend a hand of friendship to them once they stop the slandering, or simply ask them out for coffee. Be there for them when they need some sort of help and always talk politely to them. If the backbiter is making no effort in hiding their hatred for you, then simply maintain a distance and if talking to them cannot be avoided, do so with respect.