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.