The primary structure that contains a cell's genetic material is the nucleus. In eukaryotic cells, the nucleus serves as the control center, housing the cell's DNA, which contains the instructions for development, reproduction, and functioning. The DNA is organized into chromosomes, ensuring that genetic information can be accurately replicated and passed on during cell division. The nuclear envelope surrounds the nucleus, protecting the genetic material and regulating the movement of molecules in and out through nuclear pores. This organization allows cells to control gene expression and manage essential cellular processes effectively.