It should be pointed out that this was February 1984, before
the advent of performers like Madonna, and audiences were
not accustomed to having sexual hot buttons pushed and
challenged this way by "pop stars".  Reportedly, the stunned
and slightly confused audience didn't quite know what to do
when the performance ended, leading bemused show host
John Denver to comment that he could have sworn there was
a girl there during rehearsals.  To view the video, click
Eurythmics on the 1984 Grammy Awards
A legendary performance is born - February 28, 1984
F  E  A  T  U  R  E  S
1984 - the American music scene is enjoying what the press
dubs "the second British invasion" (referring to the original
British invasion of the 1960s which saw the rise of such
supergroups as the Who, the Rolling Stones and the
Beatles).  Enjoying immense popularity on the then-new
medium of MTV, as well as significant support from U.S. radio
programmers, bands such as Eurythmics, Duran Duran and
Culture Club spearheaded the musical invasion from the U.K.  
Not only known for great songwriting, singing and playing,
these new bands possessed a facile gift to use visual media to
get their ideas across.  The video clips from these bands were
ground-breaking and highly influential.   
Eurythmics are enjoying immense popularity in the U.S. after
the #1 success of their single "Sweet Dreams (Are Made of
This)".  The  eye-catching video (as well as their other video
"Who's That Girl?") quickly led the press to dub the band as
"gender benders" because of Annie Lennox's various looks.  
While not quite the whole story, Eurythmics did perform a slyly
tongue-in-cheek response to all this by doing "Sweet Dreams"
live on the 1984 Grammys with Annie decked out in male drag
(or dressed as the alter-ego known as "Earl", as Eurythmics
referred to "him" in subsequent interviews).  The performance
would become legendary amongst fans and music lovers.
The first thing one had to ask when the performance started
was "Where's Annie?"  You heard the rich, soulful voice
singing "Sweet dreams are made of this" and saw Dave
Stewart, resplendent in the coolest shimmering shirt ever
worn, but who is that guy with the suit, tie, black hair and
sideburns?  It dawns on the audience like an electric bolt -
it's Annie! - and immediately the performance becomes
transcendent.  Strutting and slyly playing for the camera,
Annie does a masterful job in her disguise.  An audience of
millions is watching this brilliantly subversive commentary
juxtaposed with a musical performance, and the sheer
impact of it all led the Grammys to include it in their video
series of Grammy's Greatest Moments.