There are no fewer than eight link homology theories which admit spectral sequences from Khovanov homology. These theories have very different origins -- representation theory, gauge theory, symplectic topology -- so it's natural to ask for some kind of unifying theory. I will attempt to describe this theory using Bar-Natan's pictorial formulation of link homology. This strengthens a result of Baldwin, Hedden, and Lobb and proves new functoriality results for several link homology theories. I won't assume much specific knowledge of these link homology theories, and the bulk of the talk will be accessible to graduate students!