In the vibrant neighborhood of Brooklyn, New York, an upright piano is being hoisted into the home of the Gershwin family, consisting of Morris, Rose, and their two sons, Ira Gershwin and young George Gershwin. Initially, Morris excitedly informs Ira about his piano lessons, but Ira expresses disdain for the idea. Their conversation takes a turn when they hear George playing a captivating tune on the piano. Impressed by his talent, Morris and Rose promptly decide to enroll George in lessons instead.
As George grows, he becomes increasingly engrossed in the bustling music scene of Tin Pan Alley. He navigates through various music teachers before settling with Prof. Franck. George showcases his talent for composing Jazz, receiving encouragement from Prof. Franck to follow his passion. He begins crafting numerous songs, but success remains elusive initially. Eventually, he secures a position as a pianist for a show featuring Harpo Marx. During the performance, he faces mockery on stage and, feeling dejected, he storms out of the theater with Ira right behind him.
Determined to pursue his dreams, George transitions to a job as a song plugger, playing tunes to potential listeners. It is here he crosses paths with Julie Adams, a talented Broadway singer. Struck by her exceptional voice, George suggests she sing his composition, "Swanee." Julie enthusiastically agrees, and this leads George to offer her his copy, alongside the other pieces he has. Soon after, he calls his boss to resign from his job.
With newfound determination, George heads to pitch his song to Max Dreyfus. While waiting, he unexpectedly meets Oscar Levant, who becomes his lifelong friend. After demonstrating his song to Max, George garners positive feedback, convincing Max to get famed singer Al Jolson to perform it. Al's extraordinary rendition generates a wave of applause, inspiring George to delve into writing his own musical, casting Julie as his leading lady because he believes she is perfect for the role. Despite the initial flop of their show, George's perseverance pays off as his musicals gain popularity, with Julie consistently in the spotlight.
As their careers flourish, Julie begins to develop feelings for George, although he remains blissfully unaware of her affections. During a backstage encounter with bandleader Paul Whiteman, George is presented with the opportunity to create a unique show that fuses Jazz with European Classical music. Tensions arise at a dinner party between Prof. Franck and Max concerning this idea, with Max urging George to stick to writing popular hits while Franck encourages him to follow his heart. Ultimately, George embraces the challenge and composes Rhapsody in Blue. He performs his piece at the premiere, where luminaries like Igor Stravinsky and Sergei Rachmaninoff are in attendance, and his work is met with widespread acclaim, marking a significant milestone in his career.
After the successful performance, George attempts to visit Prof. Franck, only to discover that the professor is gravely ill and unable to attend. Shortly after, he is approached to write a Concerto for the New York Philharmonic, to be showcased at Carnegie Hall; however, George hesitates due to his perceived lack of experience with classical composition. As he continues to juggle musicals, he notices Ira's developing skill as a lyricist and entrusts him with the lyrics for his next show, Lady be Good, which becomes a phenomenal success.
Seeking further inspiration for his concerto, George travels to Paris where he hears his own song, Fascinating Rhythm, being played in a lively nightclub. During his visit, he meets Christine Gilbert, and they quickly develop a romantic relationship filled with delightful adventures. When George invites Christine back to America for a party, Julie's heart sinks upon seeing them together. At the gathering, George and Ira affectionately nickname each other "Mr. Words" and "Mr. Music." During a special moment, George plays The Man I Love on the piano, accompanied by Julie's singing. However, overwhelmed with emotions, Julie suddenly departs without a word, leaving George bewildered.
In the aftermath, George becomes captivated by painting and begins to dedicate time to the canvas. One day, Christine walks in on him and professes her love, prompting George to dream of a shared future in a penthouse in New York. Dismayed, Julie remarks that he "sounds like his songs," and after a tense exchange, she leaves, her heart aching from the longing that remains unresolved.
