Children’s rights to asylum have emerged as an urgent political challenge. This article uses a number of cases discussed in Sweden’s largest morning paper to analyse claims of asylum-seeking children and how these claims challenge the normative limits of contemporary asylum, concerning what and who ought to be recognized by law. Even though the universality of the child constitutes a running theme, the arguments and the conception of children underpinning the claims are diverse. The article suggests that the claiming of rights as a socio-political practice could be a vital analytical approach to studying children’s rights and offers a much needed alternative to the dominant mainstreaming paradigm.