Searches for very weakly-coupled particles beyond the Standard Model with NA62

The NA62 experiment at CERN is designed to measure precisely the rare decay $K^{+} \rightarrow \pi^+ \nu \bar{\nu}$. The intensity and energy of the SPS proton beam used to produce the $K^+$, as well as the hermetic detector coverage and overall geometry, give in addition the opportunity to search for hypothesized weakly-coupled particles at the MeV-GeV mass scale. In these proceedings the focus lies on reviewing these opportunities and sketching the current status of some pertinent searches.