Lipshitz and Sarkar recently constructied a stable homotopy refinement of Khovanov homology using Cohen-Jones-Segal Morse theory. In this talk, I will discuss an alternate proof of their result which uses more stable homotopy theory instead (a joint work with Po Hu and Daniel Kriz). I will also relate this to a previous weaker result of ours, and to homotopical realizations of modular functors.