Taylor and Burton on the set of 'Cleopatra'

There are Hollywood romances, and then there are superstar romances, and no superstar romance ever managed to cram as much scandal, star power and unabashed sexual attraction into one gaudy package as the affair, marriage, divorce, second marriage and second divorce of Elizabeth Taylor and Richard Burton. Their tumultuous liaison — before the marriages and divorces — famously began in 1962 on the set of the colossally over-budget epic, 'Cleopatra'. Fodder for gossip columns and tabloids, all these years later their affair remains the gold standard for famous folks behaving badly on movie sets. (Of course, their behavior seems downright quaint, and even circumspect, compared to the squalid hijinks of many of today's celebs.)
Here, on the 50th anniversary of the movie's June 12, 1963, release in the U.S., LIFE presents a series of photographs — most of which never ran in LIFE — made on the Roman set of 'Cleopatra' by photographer Paul Schutzer.