I will discuss some current work (with Garner, Hilburn, Oblomkov, and Rozansky) on new and old constructions of HOMFLY-PT link homology in physics and mathematics, and new connections among them. In particular, we relate the classic proposal of Gukov-Schwarz-Vafa, involving M-theory on a resolved conifold, to constructions in $3d$ TQFT's. In the talk, I will focus mainly on the $3d$ part of the story. I'll review general aspects of $3d$ TQFT's, in particular the "$3d$ A and B models" that play a role here, and how link homology appears in them.