The two actors met on the set of the film Stakeout and got married on the 21st November 1987 at the Golden Nugget Hotel in Las Vegas Nevada.
They had three daughters together: Rumer (1988), Scout LaRue (1991) and Tallulah Belle (1994) before they separated on 18th October 2000. They never revealed why they spilt, however Willis publicly thanked actor Will Smith for helping through his divorce. Willis later said; "I felt I had failed as a father and a husband by not being able to make it work." (Wikipedia)
Rumours escalated that they might get back together, however these were dispelled when Moore married Ashton Kutcher. Willis attended their wedding on 24th September 2005 along with other close friends and family.
Source: Wikipedia and IMDB.