It’s wonderful to watch young people falling in love for the first time. That’s why we get to see it so often in the movies. But it is even more wonderful to see people falling in love for the last time, and that is one of the three great pleasures of this touching grown-up love story.

It’s always romantic to see first love because we can share with them — just for a moment — the belief that happily ever after means that there will never be an argument or disappointment or loss. But it is even more romantic to see older people fall in love because they know there will be all of that and they go ahead anyway. That is the story of “Last Chance Harvey,” a man who has lost his job and whose daughter asks her step-father to give her away at her wedding because she feels closer to him. Which is what gives him a chance to think about what he really wants for the rest of his life — and then he sees Kate.

Not much more happens. They walk around. They dance at the daughter’s wedding reception. They think about whether they really want to take the risk of sharing themselves knowing in a way that young people cannot what it really means. And yet in those moments, everything happens, and we know it and they know it.

The other two pleasures of the film are Dustin Hoffman as Harvey and Emma Thompson as Kate. These two actors, so perfectly at home with themselves, fearlessly give us two people who are complicated, difficult, and very, very protective of their bruised hearts. And then they let us see them bloom, not all at once, more of a two steps forward, one step back opening up of their hearts to each other. And that leaves our hearts just a little more open, too.