Today, 95% of the global population has 2G mobile phone coverage and the number of individuals who own a mobile phone is at an all time high. Mobile phones generate rich data on billions of people across different societal contexts and have in the last decade helped redefine how we do research and build tools to understand society. As such, mobile phone data has the potential to revolutionize how we tackle humanitarian problems, such as the many suffered by refugees all over the world. While promising, mobile phone data and the new computational approaches bring both opportunities and challenges. Mobile phone traces contain detailed information regarding peoples whereabouts, social life, and even financial standing. Therefore, developing and adopting strategies that open data up to the wider humanitarian and international development community for analysis and research while simultaneously protecting the privacy of individuals is of paramount importance. Here we outline the challenging situation of children on the move and actions UNICEF is pushing in helping displaced children and youth globally, and discuss opportunities where mobile phone data can be used. We identify three key challenges: data access, data and algorithmic bias, and operationalization of research, which need to be addressed if mobile phone data is to be successfully applied in humanitarian contexts.