In this article, we introduce the key themes of our Special Issue on "Transnational care: families confronting borders". Central to this collection is the question of how family relations and solidarities are impacted by the current scenario of closed borders and increasingly restrictive migration regimes. This question is examined more specifically through the lens of care dynamics within transnational families and their (re-) configurations across diverse contexts marked by "immobilizing regimes of migration". We begin by presenting a brief overview of key concepts in the transnational families and caregiving literature that provides a foundation for the diverse cases explored in the articles, including refugees and asylum seekers in Germany and Finland, Polish facing Brexit in the UK, Latin American migrants transiting through Mexico, and restrictionist drifts in migration policies in Australia, Belgium and the UK. Drawing on this rich work, we identify two policy tools; namely temporality and exclusion, which appear to be particularly salient features of immobilizing regimes of migration that significantly influence care-related mobilities. We conclude with a discussion of how immobilizing regimes are putting transnational family solidarities in crisis, including in the context of the Covid-19 pandemic, gripping the globe at the time of writing.