  We provide a pedagogical introduction to the concept of the local density of
optical states (LDOS), illustrating its application to both the classical and
quantum theory of radiation. We show that the LDOS governs the efficiency of a
macroscopic classical antenna, determining how the antenna's emission depends
on its environment. The LDOS is shown to similarly modify the spontaneous
emission rate of a quantum emitter, such as an excited atom, molecule, ion, or
quantum dot that is embedded in a nanostructured optical environment. The
difference between the number density of optical states, the local density of
optical states, and the partial local density of optical states is elaborated
and examples are provided for each density of states to illustrate where these
are required. We illustrate the universal effect of the LDOS on emission by
comparing systems with emission wavelengths that differ by more than 5 orders
of magnitude, and systems whose decay rates differ by more than 5 orders of
magnitude. To conclude we discuss and resolve an apparent difference between
the classical and quantum expressions for the spontaneous emission rate that
often seems to be overlooked, and discuss the experimental determination of the
LDOS.
