How is the current progress on rationality problem for complex hypersurfaces $X\subset\mathbb{P}^{n+1}$ with $n\geq 3$?

There are many hypersurfaces are shown to be unrational, such as smooth cubic threefolds and smooth quartic threefolds. Hypersurfaces with degree $d$ large enough are known to be unrational (they are not even uniruled when $d>n+1$).

However, there are only a few examples of rational hypersurfaces.

• A singular cubic hypersurface which is not a cone is ratinoal.
• Some special cubic fourfolds are rational (many people). Moreover, a smooth cubic hypersurface $X\subset\mathbb{P}^{2n+1}$ containing two skew linear spaces of dimension $n$ is rational.

Are there any new examples in recent years? Or did I miss some known examples?