Endocytosis and Exocytosis.

Endocytosis is a form of cellular transport where cells absorb molecules or substances from outside the cell by 'engulfing' it with the cell membrane. This process allows larger particles that can’t enter the cell by any other means to enter the cell. Each case of endocytosis results in the formation of an intracellular vesicle. Every cell of the body undergoes endocytosis, as most substances important to them are larger molecules, which cannot pass through the cell membrane or hydrophobic plasma.
Figure 1: The processes of endocytosis and exocytosis

There are three types of Endocytosis:
Phagocytosis, which translates to “cell eating”, is where the cell membrane folds around the molecule or substance, isolating it for later use in a vacuole called a phagosome.
Pinocytosis, which translates into “cell drinking”, where the cell membrane folds around the molecule or substance, but instead of storing the substance in a phagosome, it dissolves into the interior of the cell. This process is used when the cell is ingesting molecules such as proteins and other water-soluble substances, which would have no other way of breaching the membrane.
Receptor-Mediated endocytosis, is much like phagocytosis, except it uses receptor proteins embedded in the cell membrane. These receptor proteins target specific substances, grasp them and drag them into a fold of the cell membrane. Cholesterol being absorbed into our blood stream is an example of this process.

Exocytosis, is the reverse process of endocytosis, it removes intracellular vesicles such as substances and molecules from the cell that are too large to pass through the cell membrane or hydrophobic plasma. Exocytosis can be consecutive or regulated. This means it can either be occuring all the time, or triggered from an external signal.
The process of exocytosis involves five steps:
Vesicle Trafficking, where the vesicle containing the waste product or chemical transmitter is transported through the cytoplasm towards the part of the cell from which it will be eliminated.
Vesicle Tethering, is where the vesicle approaching the cell membrane is secured and dragged towards the site where it will be eliminated.
Vesicle Docking, this is where the vesicle begins to come in contact with the cell membrane, and it chemically and physically fuses with the proteins in the membrane
Vesicle Priming, this step is where the cells with chemical transmitters being released, are preparing for the last stage of exocytosis.
Vesicle Fusion, in this step the proteins forming the walls of the vesicle merge with the cell membrane and breach, pushing the vesicle waste products or chemical transmitters out of the cell.

Click for an Animation of Endocytosis and Exocytosis