Sean Penn in the style of Robert Smith would, initially, come across as a comedy, however Paolo Sorrentino's This Must Be The Place is much more on the existential drama side. Exploring the ennui of fame twenty years after you peak, Sorrentino and Umberto Contarello's script is a departure from your usual movie about the pratfalls of notoriety. Perhaps because it is a French/Italian/Irish co-production, This Must Be The Place is allowed to take its time with pacing and establishing a theme--while also creating a genre of its own, that of the rock and roll Holocaust mystery. Cheyenne's (Penn) once profitable career as a macabre frontman has quickly devolved into mental atrophying in his palatial Dublin home with his wife, Jane (Frances McDormand, the natural go-to when you want to cast a quirky spouse). Part poet, part philosopher, Cheyenne spends his time spouting aphorisms like, "No one works but everyone's doing something artistic" and "We go from saying 'That's gonna be my life' to 'That's life.'"
He also spends his time hanging out with a lookalike acolyte named Mary (Eve Hewson a.k.a.Bono's daughter), whether it's at the mall or at one of their houses. It is while they are sitting together at a coffee shop after seeing a band called the Pieces of Shit that Mary is pursued by a blue collar type named Desmond (Sam Keeley). Assuming that Cheyenne is her father, Desmond asks his permission to take Mary out. Cheyenne quickly corrects the assumption and then lets Mary make the decision for herself--that decision being a swift rejection on the basis of his musical interests. Cheyenne then makes it one of his pet projects to get what he calls "one sad girl" and "one sad boy" together. His other main activity includes playing handball with Jane in their unfilled pool. When Desmond inquires as to why no one ever bothered to fill the pool, Cheyenne's more divaish side comes out, causing him to snap and say that it simply never did--there's no reasoning behind it. In many ways, the plot points of This Must Be The Place itself have no reasoning behind them either. But that's not necessarily a bad thing.
As Cheyenne starts to reconcile how dissatisfied he is with his life--an epiphany that comes after eating out Jane--he becomes more attached to Mary's home life situation. Her brother's disappearance three months prior has left Mary's mother practically catatonic, refusing to leave the window facing the street where he might return. One day while visiting them, Cheyenne receives a call about the death of his father, whom he had not spoken to in thirty years. With a sudden burst of purpose, Cheyenne is motivated to go to New York to handle his father's Estate, where, among other life-altering events, he learns that his father was on a lifelong quest to find and take vengeance on a Nazi that humiliated him at Auschwitz. And then there's the performance of David Byrne (playing himself with an especially Jim Jarmusch hairstyle) singing the song for which the film was named. After watching him play with such enduring talent and ability, Cheyenne has a breakdown after the show when talking to Byrne, lamenting that he never had any real talent, but was merely capitalizing on an 80s trend of depression and angst. His music, he feels, was also the direct cause of two teen suicides at the height of his popularity. So racked with guilt over their deaths, Cheyenne continues to visit their graves every week--though he says it tends to make him feel guiltier instead of better.
Arriving in New York too late to say goodbye to his father, Cheyenne consults with Mordecai Midler (Judd Hirsch), a Nazi hunter that Cheyenne’s father employed to find Aloise Lange (Heinz Lieven). Determined to carry out his father’s mission to find Lange and make him pay for the shame he caused, Cheyenne starts by going to Lange’s wife, Dorothy (Joyce Van Patten), the only link that Mordecai ever found to Lange. Posing as a former student (she was, appropriately, a history teacher at one point), Cheyenne bides his time visiting with her to see what information he can glean and then returns in the middle of the night to find the whereabouts of her granddaughter, Rachel (Kerry Condon). The mystery continues to unfold when he finds her, ultimately using his sleuthing skills to get a little too close to her and her son.
Never actually addressing why Robert Smith is the model for Sean Penn’s aesthetic (though I suppose he’s the only aging pop star to continue the commitment to his original look) , This Must Be The Place chooses not to explain very much at all, leaving it up to the viewer to make his or her own meaning from the story, which, if nothing else, is chock full of poignant quotes and amazing music.