What are recent advances in relational databases?
In db query area arguably Provenance Semiring enjoyed the most attention recently. The "provenance" adjective is just marketing connecting it to a large body of research. Nevertheless the idea that one may have much more elegant mathematical foundation for database query languages is compelling. My personal view is that semiring perspective (which works wonders in formal language theory) has to be complemented with Relational Lattice.  

Here is another view of what happened in the last decade. (The speaker holds a record of continued PODS admittance:).

On less theoretical note lets mention Dedalus, and plenty of Tutorial D enthusiasts; both, however, are hardly the recent ideas.