Although The Cure had been well established in the UK, this was the song that broke them to a bigger US audience. This song has also stood up to a wide variety of treatments in cover versions.
Released as the third single from Kiss Me, Kiss Me, Kiss Me, this brought The Cure the sort of popularity in the US that they already had in Europe.
Totally worth watching is Rick Beato’s analysis of Just Like Heaven in his ’What Makes This Song Great’ series which pulls apart the song part by part, instrument by instrument. Check it out - it’s why I’m keeping this write-up short - he says it better than I can.
Popular (though I’m not much of a fan of it) is a fairly faithful cover by Dinosaur Jr..