  We review the use of emission-lines for understanding galaxy evolution,
focusing on excitation source, metallicity, ionization parameter, ISM pressure
and electron density. We show that the UV, optical and infrared contain
complementary diagnostics that can probe the conditions within different
nebular ionization zones. In anticipation of upcoming telescope facilities, we
provide new self-consistent emission-line diagnostic calibrations for complete
spectral coverage from the UV to the infrared. These diagnostics can be used in
concert to understand how fundamental galaxy properties have changed across
cosmic time. We describe new 2D and 3D emission-line diagnostics to separate
the contributions from star formation, AGN and shocks using integral field
spectroscopy. We discuss the physics, benefits, and caveats of emission-line
diagnostics, including the effect of theoretical model uncertainties, diffuse
ionized gas, and sample selection bias. Accounting for complex density
gradients and temperature profiles is critical for reliably estimating the
fundamental properties of H ii regions and galaxies. Diffuse ionized gas can
raise metallicity estimates, flatten metallicity gradients, and introduce
scatter in ionization parameter measurements. We summarize with a discussion of
the challenges and major opportunities for emission-line diagnostics in the
coming years.
