The NDR series robot "Andrew" (Robin Williams) is introduced into the Martin family home in April 2005 to perform housekeeping and maintenance duties. The family's reactions to the new convenience range from acceptance and curiosity to outright rejection and deliberate vandalism, which leads to the discovery that this robot can both identify emotions and reciprocate in kind. When Andrew accidentally breaks a glass figurine belonging to "Little Miss" Amanda Martin (Hallie Kate Eisenberg), to whom he is devoted, he carves a similar figurine out of wood. The family is astonished by this sign of original creativity in a robot and “Sir” Richard Martin (Sam Neill) takes Andrew to his manufacturer, NorthAm Robotics, to inquire if all the robots are like him. The CEO of the company sees this development as a problem and wishes to scrap Andrew or, as he puts it, "fix him." Angered, Martin takes Andrew home and allows him to pursue his own development: creating masterpiece clocks and other wood items. He also encourages Andrew to educate himself in the humanities and helps him to understand the concepts.

Many, many years have passed, and Amanda is grown up. While working on the Martins' basement, Amanda talks with Andrew, and yells his name from behind. Andrew gets surprised, and his right thumb is accidentally cut off. Martin again takes him to NorthAm Robotics for repairs, ensuring first that Andrew's personality will remain unharmed. Andrew requests that while he is being repaired his face be altered to convey the emotions he feels but cannot fully express; after the repairs Andrew is able to show a wider degree of facial expression including smiling. Through the years, Andrew has amassed enough money to need a legal adviser and bank account. Andrew eventually asks for his freedom, much to Richard's dismay. Deeply hurt, Mr. Martin grants his request, but banishes Andrew from the house so that he can be 'completely' free, once Andrew is free he starts to refer to himself as "I" rather than "one," as Andrew has done during the years. With his money Andrew builds himself a home and lives alone. In 2048, Andrew sees Richard Martin one last time on his deathbed. Mr. Martin apologizes to Andrew for banishing him, telling him it was Andrew's right to have his freedom.

Andrew sets out to find other NDR series robots and discover if they have also developed personalities of their own. He spends years searching, but finds none functioning. Finally, he stumbles across Galatea, a NDR robot that has been given female attributes and personality, but these are simply part of her programming and not developed like Andrew's is. Galatea is owned by Rupert Burns (Oliver Platt), son of the original NDR robot designer. As it turns out, Burns has been working to create a more human looking robot on his own, but has been unable to attract funding for the project. Andrew agrees to finance Burns' research and the two join forces to revolutionize robotics. As part of this research, Andrew designs new artificial prosthetic organs for the robots that could also be used for humans. Over the years, he maintains contact with Amanda, who grows up, marries, divorces and dies. Eventually, Andrew becomes human enough to fall in love with Amanda's granddaughter, Portia (both played by Embeth Davidtz), and she with him.

Now possessing artificial skin and hair, Andrew petitions the World Congress to recognize him as human, which would allow him and Portia to be legally married, but is rejected: he is still immortal and thus cannot be considered human. Over the course of the next century, he proceeds to turn himself into a prosthetic human complete with a nervous system and blood, and begins to age alongside Portia. Andrew again attends the World Congress, now appearing old and frail, and again petitions to be declared a human being. The new Speaker of the Congress (Lynne Thigpen) agrees to debate the issue and asks him why he wants this. Andrew replies: "To be acknowledged for who and what I am; no more, no less. Not for acclaim, not for approval, but the simple truth of that recognition has been the elemental drive of my existence and it must be achieved if I am to live or die with dignity."

Andrew is on his death bed, Portia beside him, when the Speaker of the World Congress finally announces on television the court's decision: that Andrew Martin is now officially recognized as human, and the oldest human being in history, aged two-hundred years old. The Speaker also finally validates the marriage between Portia and Andrew. Andrew dies while listening to the broadcast, and Portia orders their nurse, a now recognizably human Galatea, to unplug her life support machine. The movie ends with Portia about to die hand-in-hand with Andrew, as she whispers to him "See you soon."