This paper reviews almost three decades of work on atlasing and segmentation methods for subcortical structures in human brain MRI. In writing this survey, we have three distinct aims. First, to document the evolution of digital subcortical atlases of the human brain, from the early MRI templates published in the nineties, to the complex multi-modal atlases at the subregion level that are available today. Second, to provide a detailed record of related efforts in the automated segmentation front, from earlier atlas-based methods to modern machine learning approaches. And third, to present a perspective on the future of high-resolution atlasing and segmentation of subcortical structures in in vivo human brain MRI, including open challenges and opportunities created by recent developments in machine learning.