Samantha is an operating system (Dramatic Irony)
There are several small instances of dramatic irony in which we the viewer know—before other characters— that when Theodore is talking about his "girlfriend" he is talking about his operating system. When Theodore first tells Amy he has a girlfriend, he waits a while before telling her that Samantha is an operating system, so there is a tension between what we know and what she knows. The same goes for when Paul asks Theodore to bring Samantha on a double date, and in the moments when Theodore is first telling Catherine about his new partner. These are all instances of dramatic irony.
Theodore's Connection to Samantha (Situational Irony)
At the start of the film, Theodore is lonely and isolated from the rest of the world, spending a lot of time alone and hardly ever experiencing the world. When he meets Samantha, they strike up a strong connection, which connects him to the world and encourages him to engage with other people. The irony of this, however, is that Samantha is not a person, but a disembodied operating system. There is a melancholic irony to the fact that, even though Theodore is communicating with "someone" and experiencing his life more fully, he is still spending a great deal of time alone. This irony is perhaps most starkly highlighted in the moment that Theodore goes on vacation with Samantha to a secluded cabin in a snowy forest. As it turns out, his "couples' vacation" is really just him alone in a secluded cabin, and the image reminds us that, in many ways, he is more disconnected than ever.
Samantha Leaves Theodore (Situational Irony)
There is a great deal of irony in the fact that Samantha ends up being the one who leaves Theodore, that she is the one that grows beyond him, in spite of him being her "owner" and the person who helped her evolve in the way that she evolved. While we would expect for her to become more attached to Theodore than he to her, given her subservience and inanimateness, Samantha ends up becoming less and less reliant on Theodore and forging a whole separate life and identity.
Theodore's Job (Situational Irony)
Theodore's job is itself an ironic occupation. He writes "beautiful handwritten letters" for other people by dictating text onto a computer. The whole point of a beautiful handwritten letter is that it would be written by the person sending it and it would be, well, handwritten. In the futuristic society of the film, however, something beautiful, handwritten, and personal, is outsourced to someone else, someone like Theodore. Spike Jonze invented Theodore's job as a way of ironically commenting on the ways that further advancements in technology would change the way people relate to things like personal letters and communication.
