The last year has brought many new insights into the algebraic and geometric structures of B-series (and family and friends, such as Lie-Butcher and equivariant series). It is exciting to see that the classical theory is now tied closely both to central concepts of differential geometry (connections on Lie algebroids) as well as to representation theory (Schur-Weyl duality and invariant tensor theorem). We will give an exposition of these new developments, and discuss (still) open problems.