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We present a list of problems related to the study of Thurston metric on Teichmüller space. The problems originate in discussions by the participants at the 2012 AIM workshop “Lipschitz metric on Teichmüller space”. Some of the problems were worked on by small groups, and they remain open. Some others were suggested by various participants at the closing problem session of the conference or added after the conference. We have updated the list in order to include it in the present Handbook.