This church is an architectural and artistic gem, barely a 5 minute walk from the Duomo. As of this writing (Winter 2015/16) t's undergoing HEAVY construction but if you've never seen it, and have the opportunity (even under construction) this should be on everyone's "must see" list.
There's a courtyard leading into the church, from the street outdoors, which is completely off limits because of a full-scale restoration but it containts frescos by all the masters of Mannerism; Del Sarto, Pontormo, Alori... they're all represented here. The main cathedral itself is stunningly beautiful. I was fortunate to stop by during the hour preceeding sunset and witnessed a brilliant display (almost a performance) of natural lighting.
The current church was originally built in 1444 which makes it full-on Renaissance style architecture. There was, however, an earlier church standing here dating back to 1250. That earlier church was founded by 4 of the original order of the Servites and the church is considered the mother church of the Servite order of monks. It's official designation is a minor basilica.
It gets it's name Santissima Annunziata (blessed annunciation) in 1252, shortly after the first church was completed, when one of the founding brothers was decorating the wall of the cathedral with a fresco depiction of The Annunciation but abandoned it in a wave of artistic angst. While he slept, an angel supposedly came and finished it. That's the story. Must be true. Over the years it's been renovated and redesigned several times. Most notably during the Baroque (1600s) period... but in my humble opinion those modifications just add to the character. I'm not an architectural purist; I can understand 400 or 500 years changing the look and feel of a partucular space. This is a spellbinding, wonderful, and beautiful basilica. Well worth a visit if you find yourself in Florence.