Residual finite dimensionality is the C*-algebraic analogue for maximal almost periodicity and residual
finiteness for groups. Just as with the analogous group-theoretic properties, there is significant interest in when residual finite
dimensionality is preserved under standard constructions, in particular amalgamated free products. In general, this question is quite difficult; however the answer is completely understood when the amalgamated subalgebra is finite dimensional. In this talk, I will discuss recent progress in understanding amalgamated products of RFD C*-algebras over central subalgebras. The material is based in part on joint work with Tatiana Shulman.