Polarised and entangled hyperons provide a powerful diagnostic tool to study the strong interaction and to search for physics beyond the Standard Model at the precision frontier. The BESIII experiment in China offers unique possibilities to study strange hyperon-antihyperon final states under particle-antiparticle-symmetric conditions. Recent results include the first complete measurement of the time-like structure of any baryon, as well as a precise charge conjugation and parity test for the $\Lambda$ hyperon. Both analyses exploit the self-analysing weak decay of hyperons, giving access to spin polarisation and entanglement of the hyperon-antihyperon pair. Using a similar approach, we can gain new information on production and decay of a number of single- and multi-strange as well as charmed hyperons. These proceedings present a summary of the most recent findings and give a glimpse into ongoing studies of which new results are expected in the near future.