  We survey some recent progress on the deformed Hermitian-Yang-Mills (dHYM)
equation. We discuss the role of geometric invariant theory (GIT) in
approaching the solvability of the dHYM equation, following work of the first
author and S.-T. Yau. We compare the GIT picture with the conjectural picture
for dHYM involving Bridgeland stability. In particular, following Arcara-Miles,
we show that on the blow-up of $\mathbb{P}^2$ any line bundle admitting a
solution of the deformed Hermitian-Yang-Mills equation is Bridgeland stable,
but not conversely. Finally, we survey some recent progress on heat flows
associated to the dHYM equation.
