Here are three things about gravity--one problem, one fact, and a piece of lore: (1) Gravity is the only known force, which is not understood on the quantum level. (2) Gravity is "holographic": a gravitational system can be recast as a one-lower-dimensional field theory without gravity. (3) The structure of gravity, perhaps its very essense, appears deeply rooted in quantum information theory, cf. Hawking's conclusion that a black hole's entropy is its surface area. Statement (3) suggests a strategy to address problem (1) and understand gravity: to examine information theoretic properties of the holographic descriptions of gravity stipulated in (2). That is, we ask what is special about gravity, and look for answers in quantum information theory using holography. It turns out that the gravitational interpretation imposes a set of novel inequalities on von Neumann entropies of reduced states; such inequalities are set to delimit the "holographic entropy cone." I will review known facts about the cone (work by others, going back to 2015) and sketch recent progress on this question, done in my group here at Tsinghua. A salient feature of the holographic entropy cone is the prominent role played by absolutely maximally entangled (perfect tensor) states. I hope we will discuss together the significance of this and related facts for understanding gravity. The main tentative lessons involve viewing gravitational spacetimes as error-correcting codes and interpreting free fall as (a generalization of) Schumacher compression.