I will discuss how novel ideas from non-abelian  Brill-Noether theory coupled with tropical geometry can be used to prove that the moduli space of  genus 16 is uniruled. This is the highest genus for which the moduli space is known not to be of general type. For the much studied question of  determining the Kodaira dimension of $M_g$, this case has long been understood to be crucial in order to make further  progress.  This is joint work with Verra