In this talk, I address the problem of fairly allocating $m$ indivisible items among $n$ agents with diverse preferences, focusing on the maximin share (MMS) fairness criterion. The MMS represents the minimum value an agent can guarantee for themselves by partitioning the items into $n$ bundles and receiving the least preferred one. While prior work established the existence of a ${1}/{\log m}$-approximate MMS allocation under subadditive valuations, this guarantee becomes impractical as $m$ grows. I present recent advancements that significantly improve this approximation factor for subadditive valuations.