Language evolution has long been researched. I will review a number of broad, emerging research directions which arguably have the potential to contribute to our understanding of language evolution. Emerging topics in genomics and neurolinguistics are explored, and human-specific levels of braincase globularity – and the broader process of self-domestication within which globularity seems capable of being encapsulated – will be argued to be the central pillars of any satisfactory and interdisciplinary model of language evolution.