The issue of migrants convicted or suspected of serious criminality is one that has been high on the media and political agenda in the United Kingdom in the past two decades. This article focuses on three categories of (suspected) criminal migrants – foreign national offenders, individuals considered to pose a security risk, and those excluded from refugee status under Article 1F of the Refugee Convention – outlining the scale and demographic of these groups in the United Kingdom, governmental measures taken to facilitate their removal and the consequences for those that nevertheless remain. This examination reveals that, despite the UK’s emphasis on removal, legal obstacles and administrative problems continue to frustrate many attempts to remove such persons. As a result, large numbers of individuals are released into the community or remain in detention for often prolonged periods of time. In the case of excluded asylum-seekers, these individuals are subject to an extremely precarious form of leave. The result is these “undesirable” migrants remain in a form of “limbo”, with no firm legal status and the prospect of removal ever present. If the emphasis remains on removal rather than looking to alternative in-country solutions that are more than temporary in nature, a viable solution to this issue is likely to remain elusive.