The process by which foreign particles invading the body or minute food particles are engulfed and broken down by certain animal cells (known as phagocytes). It is a form of endocytosis in which the plasma membrane of the phagocyte invaginates to capture the particle and then closes around it to form an acidified vesicle (phagosome). This then coalesces with a lysosome, which contains enzymes that break down the particle, forming a phagolysosome. Compare pinocytosis.