The 3 main institutions of the EU are each headed by a president:
Term: August 2014 - January 2017
Elected by: Members of the European Parliament
Term: December 2014 - May 2017
Appointed by: national leaders (heads of state or government of EU countries).
Term: November 2014 - October 2019
Appointed by: national leaders (heads of state or government of EU countries), with the approval of the European Parliament.
The Council of the EU - where national ministers discuss EU legislation - doesn't have a permanent, single-person president. Its work is led by the country holding the Council presidency, which rotates every 6 months. For example, representatives from the presidency country chair its meetings.
Through its Spitzenkandidaten process, Europe has brought EU Commission presidency elections out from behind closed doors, placing power in the hands of citizens.