Skew Howe duality is based on a very simple observation: the set of n by m matrices has commuting action of SL_n and SL_m. We can use this observation to study morphisms of GL_m representations using GL_n. This perspective has proven very useful in recent years for studying quantum knot invariants and their categorifications. I will survey work in this direction from the last 10 years, including more recent developments concerning annular skew Howe duality and annular knot invariants.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/8224