Kostner won the first World Ladies title (2012) as well as the first European Ladies title for Italy in history (in 2007). She is the first Italian lady to medal at World Championships (bronze in 2005) since Susanna Driano took the bronze medal at the 1978 World Championships. Kostner is also the first Italian single skater to win a medal at Junior Worlds (bronze in 2003). She is a cousin and godchild of famous Italian skier Isolde Kostner and says she feels inspired by her. Kostner's mother Patrizia was a nationally ranked figure skater in the 1970s and her father Erwin played ice hockey on the National Italian team at World Championships and Olympic Games. Kostner has two brothers, Martin (one year older) and Simon (three years younger). Simon plays ice hockey competitively. Kostner returned to competition in December 2016 after sitting out two seasons.