Beware the subtitles. They are not much help.
Watching the film, you see each member of the household affected by the visitor in the same way, and yet the result is radically different. Each person changes as a result of their encounter; each person ends up entirely re-made -a new person, in no way the same as before- but also in no way akin to the others in the house.
Is the visitor a Christ figure?
It would definitely be worth watching again.
Moria tentatively classifies it as a fantasy. DVD Talk says, "Finding a film one does not understand can be a positive experience, but Teorema doesn't give us much reason to care. I certainly am not inspired to search for more meaning in the picture". Slant Magazine gives it 2 1/2 out of 4 stars, but I'm not sure why they rated it that high when some of their comments are, "any five minutes of any Buñuel film would make short work of Teorema," "It's all very grand and vague and shapeless ... but indulgent and fairly meaningless," and calls it "overrated and idiotic".
Roger Ebert says he doesn't know what to think about it but does venture this: "My guess is that "Teorema" is a watershed of some kind, a film out of its own time, a film nothing has prepared us for, but a film that in years to come will be seen as a turning point like early Godard" and adds this in his closing paragraph:
The sort of moviegoer who thinks all movies must make sense -obvious common sense, that is- should avoid "Teorema." Those who go anyway will be mystified, confused, perhaps indignant. But here is a film that needs additional thought.Rotten Tomatoes has an 89% critics rating.