What part of the cell allows only certain substances to pass between the nucleus and the rest of the cell?

The part of the cell that allows only certain substances to pass between the nucleus and the rest of the cell is the nuclear envelope. This double membrane structure contains nuclear pores, which are protein complexes that selectively regulate the transport of molecules such as RNA and proteins in and out of the nucleus. These pores ensure that essential substances can enter and exit while maintaining the integrity of the nuclear environment.