The Broadway production of West Side Story opened to largely ecstatic reviews 55 years ago this week, on September 26, 1957. The movie version, which went on to win 10 Oscars, including Best Picture, opened four years later, in 1961, and has been rightfully celebrated ever since as one of the most dynamic, appealing and imaginative American pop-culture creations of the 20th century.
Here, LIFE.com presents a series of photos by Gjon Mili made on the set of West Side Story. Some of these pictures ran in LIFE, while many more were not published in the magazine: but what comes across in every frame is the energy and the dedication of the men and women who were bringing a story that had already conquered Broadway to the big screen. Here, quite literally, is a classic in the making.