The film opens with a groom approaching his new bride, Sudha, on their wedding night. The bride, upon seeing the groom, screams because his face is disfigured due to burns. The groom then starts telling the bride his story and the remainder of the film is a flashback told to the bride by the groom. The story is about a boy, named Kewal (played by Shashi Kapoor), who is obsessed with theatre but is descended from a family of lawyers. Kewal is smitten by a girl named Nirmala, nicknamed Nimmi, a classmate in school when he was aged 10 years. They both enjoy theatre and Kewal shares his dream of opening a theatre company and starring in his play with Nimmi as the female lead while watching a play in their school. He soon plans to stage a play in his neighbourhood with Nimmi, but she deserts him because her family moves to a different city on the day of the premiere. The young Kewal takes this to heart, but after finishing school, Kewal (now played by Raj Kapoor) reluctantly submits to his father's (Kamal Kapoor) demands to continue the family tradition by studying law and become a successful lawyer just like him and his forefathers.

At College, Kewal meets another Nirmala (who asks him to call her Nimmi, after hearing his story of childhood love). He again plans to stage a play, but the second Nimmi also deserts him because her parents have decided to marry her off, to a man who lives in England, on the day of the premiere. Kewal is distracted and fails his law exam. This forces him to a reckoning that he has no real interest in becoming a lawyer and would like to pursue his childhood dream of owning his theatre company to write, direct, and produce plays. He argues with his father and is asked to leave the house and despite his mother's protestations, decides to chart his path in life and pursue his dreams. After a little struggle, he luckily finds a patron of the arts named Rajan, (Premnath), who is the owner of a theater company, that has closed down. Kewal and Rajan strike up a creative partnership and a friendship with Kewal writing and producing plays and Rajan financing these. During the preparation for his play, Kewal discovers a woman made homeless by Partition (Nargis) and casts her as the lead in his play.

With the finances and a leade in place, Kewal's dreams can now, at last, be realised; Kewal suggests that Nargis's character (who is not named) takes the name Nimmi (a third incarnation). Rajan is besotted by Nimmi, but Nimmi is in love with Kewal, who remains unaware of Nimmi's feelings towards him. This conflict comes to a head on the opening night of Rajan and Kewal's first production; Rajan goes berserk and rips all his pictures of Nimmi that he has painted. Kewal, only now, discovers the reality of the situation with Rajan and tries to convince Nimmi that she should get together with Rajan, who is his friend and mentor; Nimmi pleads that she is in love with Kewal and not Rajan. The play starts (with Kewal's parents, with whom he has reconsiled, in the audience) and Kewal takes a lit torch (the Aag or fire) and burns his face. During this act, of what Kewal perceives as a sacrifice to save his friendship with Rajan, the stage catches fire and the whole production company is burnt to the ground and he is disfigured.

Kewal then confronts Nimmi, who is repulsed by his disfigurement and tells her that she only liked him because of his outer beauty and only the true Nimmi liked him for who he is on the inside. Nimmi (Nargis's version) visits Kewal in the hospital with his face bandaged. Nimmi offers flowers and Kewal notices a ring on her finger which Nimmi tells is her engagement ring from Rajan; Kewal wishes her well and she slips away. The camera cuts back to the present, the wedding night, where Kewal is telling Sudha that his childhood Nimmi understood him and only she will accept him for who he is. Sudha suggests that Kewal would not know if Nimmi was standing in front of him. Sudha turns out to be the original Nimmi (from Kewal's childhood) and accepts Kewal for who he is. Kewal and Nimmi renew their vow of opening a theatre company together.