Polycyclic Aromatic Hydrocarbons (PAHs) are complex organic molecules forming on dust grains through condensation. They are usually excited by UV photons from stars and have long been used as tracers of the star forming activity in galaxies near and far. However, the chemical pathways leading to their formation (and destruction) are extremely complex and not very well understood by astronomers. In this talk I will first review the use of PAH as tracers of star formation, gas mass and/or the conditions of the interstellar medium. In an effort to shed new light on the diagnostic role of PAHs, we have initiated a new research program employing theoretically computed spectra of PAHs and examined into their properties in more detail. Our results are a taster of the vast possibilities for PAH science with the James Webb Telescope over the next couple of years.