Living creatures are made up of basic units called cells. When an organism grows or reproduces, cells undergo cell division: one cell splits into two daughter cells. Cell division requires cells to solve many physics problems to physically move their contents. For example, each daughter cell must receive one full set of the genetic material necessary for survival. This process is called chromosome segregation and is essential for successful cell division. Errors in chromosome segregation are associated with health conditions such as cancer and birth defects. Chromosome segregation in our cells is performed by a molecular machine called the mitotic spindle that exerts forces on chromosomes and moves them to the correct locations during cell division. This talk will describe the biophysics of the mitotic spindle and what we know about how it is able to segregate chromosomes. The biophysics of the mitotic spindle is also inspiring new work in which components of the mitotic spindle are taken outside of cells to make new types of biologically-inspired active materials. This work is helping us learn about the physics of nonequilibrium systems that behave in fundamentally different ways from equilibrium materials.