Migration and population aging, the two phenomena encountered by the contemporary world, are not only changing the demographic profile of the countries but also significantly influencing the structure and functioning of the families. The chapter aims to examine the nature and type of migration, vulnerabilities and strengths of the migrant elderly, and challenges and concerns faced by the left-behind older parents. Research review highlights that increasing number of people are migrating in old age, but unlike the youth who mainly migrate for better career and income options, their motives are primarily to provide care to their grandchildren and sometimes to receive sophisticated medical care. These transnational grandparents may keep on visiting back and forth or return back after their objective of visit is fulfilled. Sometimes, older people are forced to migrate owing to sociopolitical or environmental challenges. Issues and concerns of left-behind elderly were discussed in terms of their physical and mental health. Elderly who migrated as young adults either exhibit return migration or stay in host countries permanently. Suggestive measures are provided to ensure wellbeing of the migrant older persons or the empty nesters.