Daniel Huybrechts: The K3 category of a cubic fourfold – an update is a survey written on the occasion of the Compositio prize which was awarded for the paper The K3 category of a cubic fourfold. Highly recommended if you care about (or wish to be convinced about) understanding cubic fourfolds!
I can also tell you that there is a little work-in-progress coming up real soon, which was directly inspired by this survey article. Stay tuned!
We can view them as a generalization of toric Fano varieties; they should have some kind of combinatorial classification.
I look forward to seeing this classification solved!
Antonella Grassi, Giulia Gugiatti, Wendelin Lutz, Andrea Petracci: Reflexive polygons and rational elliptic surfaces is an expository and very fun-to-read note on mirror symmetry for del Pezzo surfaces.