Hazel (Shailene Woodley) and Gus (Ansel Elgort) make it to Amsterdam and meet Van Houten (Willen DeFoe), however he turns out to be an alcoholic jerk who refuses to answer any of Hazel's questions, instead teasing her for her love of his book and making light of her illness. Despite this, Hazel and Gus still have a nice day touring the Anne Frank House and make love that night for the first time.
Gus tells Hazel the next day his cancer has relapsed and is terminal. Returning to the US, Gus's health quickly declines and he holds pre-funeral he arranges to hear Hazel and Isaac's (Nat Wolff) eulogies. In hers, she tells Gus she wouldn't trade their time together for anything. She also learns that her mother (Laura Dern) is taking classes to become a speaker, and is happy that her parents will have something to focus on after she dies.
Gus dies soon after, and Hazel is heartbroken. At his funeral, she is surprised when Van Houten turns up. He apologizes for his behaviour and offers to answer her questions but she refuses and tells him to leave, crumpling up a piece of paper he gives her. Isaac tells Hazel that the piece of paper was Gus's eulogy for Hazel. She retrieves it, and reads of Gus's deep love for her, helping her to come to terms with his death and well as her eventual own.
Thanks Mark I!