  A framework of connections between asymptotic symmetries, soft theorems, and
memory effects has recently shed light on a universal structure associated with
infrared physics. Here, we show how this pattern has been used to fill in
missing elements. After the necessary groundwork, we begin by proving a Ward
identity for superrotations using the subleading soft graviton theorem, thereby
demonstrating a semiclassical Virasoro symmetry for scattering in quantum
gravity. Next, we show there exists a new spin memory effect associated with
this symmetry, explain more generally how the connections between the vertices
of the infrared triangle predicted this, and describe what other examples and
variations have been unveiled. Taking to heart this newly motivated Virasoro
symmetry, we review how the soft theorem has been recast as a Virasoro Ward
identity for a putative two dimensional conformal field theory. This derivation
relies upon a map from plane wave scattering states to a conformal primary
basis, which we then construct. We provide examples of familiar scattering
amplitudes recast in this basis and discuss the somewhat exotic nature of the
putative CFT2. We conclude by describing ongoing efforts to tame some of these
features and what this change of basis in turn has taught us about the infrared
limit which began our story.
