Multiplex genome editing is the simultaneous introduction of multiple distinct modifications to a given genome. Though in its infancy, maturation of this field will facilitate powerful new biomedical research approaches and will enable a host of far-reaching biological engineering applications, including new therapeutic modalities and industrial applications, as well as "genome writing" and de-extinction efforts. In this Perspective, we focus on multiplex editing of large eukaryotic genomes. We describe the current state of multiplexed genome editing, the current limits of our ability to multiplex edits, and provide perspective on the many applications that fully realized multiplex editing technologies would enable in higher eukaryotic genomes. We offer a broad look at future directions, covering emergent CRISPR-based technologies, advances in intracellular delivery, and new DNA assembly approaches that may enable future genome editing on a massively multiplexed scale.