With the large datasets on − + -annihilation at the / resonances collected at the BESIII experiment, multi-dimensional analyses making use of polarization and entanglement can shed new light on the production and decay properties of hyperon-anti-hyperon pairs. In a series of recent studies performed at BESIII, significant transverse polarization of the (anti)hyperons has been observed in / or to Λ Λ , Σ Σ , Ξ Ξ. The decay parameters for the most common hadronic weak decay modes were measured, and due to the non-zero polarization, the parameters of hyperon and anti-hyperon decays could be determined independently of each other for the first time. Comparing the hyperon and anti-hyperon decay parameters yields precise tests of direct, Δ = 1 -violation that complement studies performed in the kaon sector.