The natural unit system, in which the value of fundamental constants such as c and -h are set equal to one and all quantities are expressed in terms of a single unit, is usually introduced as a calculational convenience. However, we demonstrate that this system of natural units has a physical justification as well. We discuss and review the natural units, including definitions for each of the seven base units in the International System of Units (SI) in terms of a single unit. We also review the fundamental constants, which can be classified as units-dependent or units-independent. Units-independent constants, whose values are not determined by human conventions of units, may be interpreted as inherent constants of nature.