As it stands, Queen Elizabeth II is the third longest reigning monarch that is 'verifiable by exact dates'.
The current standing sees her majesty on 70 years and 117 days. She will pass Thailand's Bhumibol Adulyqdej (9th June 1946 - October 13th 2016) in ten days and then has to contend with Louis XIV, who reigned over France from May 14th 1643 to September 1st 1715 (72 years, 110 days).
Of the current living monarchs, Brunei's Sultan Hassanal Bolkiah is following Elizabeth II on that list with a reign of fifty-four years and 241 days.
That's enough research for me this morning. It'll be off by a day come this time tomorrow.