Motivated by the LHCb and BESIII hyperon programs we discuss different possibilities to constrain new physics with rare hyperon decay modes, including the rare mode $\Sigma^+ \to p\mu^+\mu^-$, charged lepton flavour violating modes, and $\Delta S=2$ modes. We review the status of standard model calculations of the processes that are allowed and illustrate the new physics windows that remain after considering the constraints that exist from kaon physics.