Taylor was convicted for his role in neighboring Sierra Leone's 11-year civil war. Taylor had perpetrated acts of terror against civilians, torturing victims, and recruiting and training armies of child soldiers. (The Sierra Leone civil war is chronicled in the film "Blood Diamond.")
The jurisdiction of the ICC extends only to cases of Crimes Against Humanity... essentially genocide and war crimes and its charter has been signed by over 120 countries. The United States has signed the charter, although has chosen to not be an official member state.
Authorities expect Joseph Konny to be tried in the ICC if and when he is captured.