I begin by appreciating the contributions in the volume that indirectly and directly address the questions: Why do gestures and embodiment matter to mathematics education, what has understanding of these achieved and what might they achieve? I argue, however, that understanding gestures can in general only play an important role in "grasping" the meaning of mathematics if the whole object-orientated "activity" is taken into account in our perspective, and give examples from my own work and from this Special Issue. Finally, I put forward the notion of a "threshold" moment, where seeing and grasping at the nexus of two or more activities often seem to be critical to breakthroughs in learning.