A long-standing open question, formalized by Blackadar and Kirchberg in the mid 90's, asks for an abstract characterization of C$^*$-subalgebras of AF-algebras. I will discuss some recent progress on this question: every separable, exact C$^*$-algebra which satisfies the UCT and admits a faithful, amenable trace embeds into an AF-algebra. Moreover, the AF-algebra may be chosen to be simple and unital with unique trace and the embedding may be taken to be trace-preserving. Modulo the UCT, this characterizes C$^*$-subalgebras of simple, unital AF-algebras. As an application, for any countable, discrete, amenable group $G$, the reduced C$^*$-algebra of $G$ embeds into a UHF-algebra.