Romance appears in several ways in Magnus Chase and the Gods of Asgard.
Mallory Keen has shown interest in the berserker. She was concerned for him during battle practice and blushed when she saw him in his underwear. She was deeply distraught when he almost died of his wounds. By the end of the book the two appear to have gotten together.
Sam and Amir are intended to marry each other. Sam has had a crush on Amir since she was twelve. When she was nervous when Magnus brought her to the food court at the transportation station and blushes when they were talking. She gets nervous when big boy holds him hostage. By the end of the book she starts to refer to him as her boyfriend.
Sam is taking flying lessons as a gift from the Fadlands. She blushes when Magnus teases her that the lesson are from Amir.
Gunilla was mentioned to have been in a relationship with a son of Loki. But it was eventually found out that he was a spy for his father. The incident left her with a deep hatred for Loki and his children.