We investigate the potential of rare hyperon decays to probe the short distance structure in the s →dv v ¯ and s → dℓ+ℓ− transitions. Hyperon decays into neutrinos (B1→B2v v ¯ ) can be reliably predicted by using form factors determined in baryon chiral perturbation theory. Their decay rates are sensitive to different short-distance operators, as compared to their kaon counterparts, and the corresponding branching fractions are in the range of 10−14 ∼ 10−13 in the standard model. In the context of the low-energy effective theory, we find that the anticipated BESIII measurements of the B1→B2v v ¯ decays would lead to constraints on new physics in the purely axial vector d ¯γμγ5s current that are stronger than the present limits from their kaon siblings K →ππv v ¯. On the other hand, although hyperon decays into charged leptons are dominated by long-distance hadronic contributions, angular observable such as the leptonic forward-backward asymmetry is sensitive to the interference between long- and short-distance contributions. We discuss the sensitivity to new physics of a potential measurement of this observable in comparison with observables in the kaon decays KL→ μ+μ− and K+→ π+μ+μ−. We conclude that the current kaon bounds are a few orders of magnitude better than those that could be obtained from Σ+→ pμ+μ− except for two scenarios with new physics in the (d ¯γμs )(ℓ ¯γμγ5ℓ ) and (d ¯γμγ5s )(ℓ ¯γμℓ ) currents. Finally, we point out that the loop effects from renormalization group evolution are important in this context, when relating the low-energy effective field theory to new physics models in the UV.