Which structure of the cell controls what goes in and comes out of the cell?

Cell membrane controls what goes in and out of the cell.

Explanation:

Cell membrane of the cell is selectively permeable to water, glucose but large molecules cannot be exchanged by cell membrane. There are specific protein channels on the cell surface which determine what goes in and out of the cell. Such as aquaporin protein channels allow smooth passage of water.

The transport of nutrients and other substances can be via osmosis, diffusion, endocytosis, exocytosis, active and passive transports.