The kinetochore drives chromosome segregation at cell division. It acts as a physical link between chromosomes and dynamic microtubules, and as a signaling hub detecting and processing microtubule attachments to control anaphase onset. The mammalian kinetochore is a large macromolecular machine that forms a dynamic interface with the many microtubules that it binds. While we know most of the kinetochore's component parts, how they work together to give rise to its robust functions remains poorly understood. Here we highlight recent findings that shed light on this question, driven by an expanding physical and molecular toolkit. We present emerging principles that underlie the kinetochore's robust microtubule grip, such as redundancy, specialization, and dynamicity, and present signal processing principles that connect this microtubule grip to robust computation. Throughout, we identify open questions, and define simple engineering concepts that provide insight into kinetochore function.