Marilyn Monroe was an American celebrity in the mid 20th century. In 1952, she met the Eleventh Doctor at a Hollywood party, and he "accidentally" accepted a marriage proposal from her. He tried to avoid it, but ended up leaving the party with her to get married, apparently making her the Doctor's spouse. Marilyn got the Doctor's phone number and later attempted to call him, though he denied the legitimacy of the chapel. (TV: A Christmas Carol)
Once, she and the Doctor had dinner. The Doctor later showed Clara Oswald a picture of this on the TARDIS scanner. (PROSE: Normality)
After Monroe was resurrected in the City of the Saved, she married Henry VIII. (PROSE: A Hundred Words from a Civil War)
River Song mentioned her among the other spouses of the Doctor. (TV: The Husbands of River Song)
When Space Pilot 692 7896 was going to die in a solo spacecraft after a total systems failure, she thought of Marilyn Monroe. Dying that way was not the glorious exit that she had expected, but she had an in-flight recorder on board of the spacecraft. She thought that she would be immortalised on camera like Monroe, James Dean and River Phoenix. (HOMEVID: Mindgame Trilogy[which?])
Other information
In HOMEVID: Good Night, the Doctor calls a farewell to an unseen River Song and asks her to "tell Marilyn she'll have to use the biplane".