All cells are surrounded by biological membranes. These are formed by phospholipids, which arrange in a bilayer where the fatty acids assemble together by hydrophobic interactions in the middle, and the charged head groups point to the aqueous media inside and outside of the cell. Proteins are inserted into this lipid bilayer. By forming channels, receptors, transporters, or other functional units, proteins contribute to diverse membrane functions, which are vital for the cell. The membrane constitutes a diffusion barrier for all hydrophilic molecules and for ions. In this chapter, it will be discussed which molecules can pass the membrane and which cannot. Due to asymmetric distribution of charged molecules at both sides of the membrane and the insulator properties of the membrane lipids, an electrical membrane potential is established in all cells. In excitable cells such as nerve and muscle cells, this potential is used for electrical signal conduction. Furthermore, we show in this chapter how proteins are co-translationally inserted into ER membranes and how they are sorted to different membrane compartments. The ER, Golgi-apparatus, lysosomes, endosomes and secretory vesicles constitute the secretory compartment of the cell. Components of this compartment travel back and forward within this compartment. All such traveling occurs by vesicle transport. Vesicles bud from their donor membrane, travel a certain distance freely or along the cytoskeleton and then fuse with a specific target membrane. Secretory vesicles can fuse with the plasma membrane and deliver their content to the extracellular space. Finally, we discuss signal transduction mechanisms for chemical signaling molecules, which cannot pass the membrane. They are bound by transmembrane receptors, which are connected to several signal transducers. These activate secondary messengers inside the cell, which instruct the cell to react to the first message delivered at the membrane.