The nearby ultra-luminous infrared galaxy (ULIRG) Arp 220 is an excellent laboratory for studies of extreme astrophysical environments. For 20 years, Very Long Baseline Interferometry (VLBI) has been used to monitor a population of compact sources thought to be supernovae (SNe), supernova remnants (SNRs) and possibly active galactic nuclei (AGNs). Using new and archival VLBI data spanning 20 years, we obtain 23 high-resolution radio images of Arp 220 at wavelengths from 18 cm to 2 cm. From model-fitting to the images we obtain estimates of flux densities and sizes of all detected sources. We detect radio continuum emission from 97 compact sources and present flux densities and sizes for all analysed observation epochs. We find evidence for a LD-relation within Arp 220, with larger sources being less luminous. We find a compact source LF $n(L)propto L^beta$ with $beta=-2.19pm0.15$, similar to SNRs in normal galaxies. Based on simulations we argue that there are many relatively large and weak sources below our detection threshold. The observations can be explained by a mixed population of SNe and SNRs, where the former expand in a dense circumstellar medium (CSM) and the latter interact with the surrounding interstellar medium (ISM). Nine sources are likely luminous, type IIn SNe. This number of luminous SNe correspond to few percent of the total number of SNe in Arp 220 which is consistent with a total SN-rate of 4 yr$^{-1}$ as inferred from the total radio emission given a normal stellar initial mass function (IMF). Based on the fitted luminosity function, we argue that emission from all compact sources, also below our detection threshold, make up at most 20% of the total radio emission at GHz frequencies.
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