The scale of Schatten-von Neumann classes is noncommutatitve analog of classical $\ell_p$-spaces. A lot of researchers devoted their lives to study Banach geometric structure of these spaces. Different geometric properties where invented along the way. Just to name a few

• The cotype and type of Banach space
• The Radon-Nykodym property
• The approximation property
• The Dunford-Pettis property
• The property of being an $\mathscr{L}_p$-space.

I would like to know if there exists any survey on noncommutative analogs of these properties. Of course I'm interested in those properties that posessed by Schatten-von Neumann classes. I doubt that such survey exists, so references to specific properties are welcomed too.