Cells are the basic unit of life. All life on earth depends on cells’ ability to make more cells. In order to divide successfully, cells must solve fascinating physics problems, which this talk will introduce assuming no biology background. A key step in cell division is ensuring that each of the daughter cells inherits a single copy of the genetic material. In eukaryotes, a machine called the mitotic spindle builds itself, then exerts forces to physically move the chromosomes. We are using theory, simulation, and experiment to address fundamental physics questions related to mitosis. These include how the mitotic spindle self organizes, how the spindle moves chromosomes, and how these same components outside of cells can create nonequilibrium materials that exhibit new physics. Microtubules are a component of the mitotic spindle that have long been known as highways for transport inside cells. I will discuss recent work which unexpectedly found that the microtubule is not a passive “road” on which motors move, but instead a responsive medium that allows motors to "talk" to each other over surprisingly long distances.