The process by which animal cells internalize particulate material (such as cellular debris and microorganisms), macromolecules (such as proteins and complex sugars), and low-molecular-weight molecules (such as vitamins and simple sugars). The size difference among these different nutrient sources requires cells to develop a hierarchical plan for endocytosis. Thus, cells engage in at least three different types of endocytosis: phagocytosis where cells engulf particulate material, receptor-mediated-endocytosis of macromolecules, and potocytosis of small molecules.