Kim Ki-Duk is a very prolific director, and sometimes falls short as a result of it, but this is a perfectly realised fable. It's not a film to be approached in any spirit of realism, except Magic Realism.
I won't go through the plot which is summarised elsewhere, but its simplicity allows for a kind of poetry of composition and a wonderfully fluent deliberate pacing which is quite hypnotic. As mentioned elsewhere, there is very little dialogue, and the heroine's silence (and almost impossible beauty) gives her a kind of mystery and allure which resonates beyond the immediate.
I don't see the lack of dialogue as any kind of weakness. The two central characters have lived together on a tiny boat for ten years, they have gone beyond words, and so when the cracks appear with the appearance of Youth, Progress, "Civilisation", at the time they might need words, they can't find them. This fuels the tragedy.
Kim revisits themes and situations he had previously used in "The Isle" The Isle [2000
], a more extremely violent movie, but there are arbitrary plot elements there and a kind of glib pessimism about the impossibility of love. Here love and growth are painful, but possible, and the final renunciation by the old man is - yes - magical, as Age gives way to Youth, as it surely must.
A beautifully crafted and coherent vision, made with the most economical of means, a handful of actors, a single location. The images will stay with you.
This went straight into my personal Top Ten Best Films ever, replacing Kurasawa's "Throne of Blood". Yes, it's that good.