This article presents a thorough discussion of the trajectories of international migration research in HCI. We begin by reporting our survey findings of 282 HCI-related publications about migration from nine digital libraries between 2010–2019, summarizing how this research stream has evolved, the geographies and populations it encompasses, and the methodologies it utilizes. We then augment these findings with data from interviews with 11 skilled researchers who reflect on their working experience in this area. Our analysis reveals how the domain has evolved from the European migrant crisis to a more global agenda of migration and points towards a shifting focus from addressing immediate needs to acknowledging more complex political and emotional aspects of mobility. We also uncover the critical role of academic, local, and international politics in migration research in HCI. We discuss these findings to explore future opportunities in this area and advance HCI research discourse with the marginalized populace.