  These notes provide an introduction to the stable homotopy types in Khovanov
theory (due to Lipshitz-Sarkar) and in knot Floer theory (due to
Manolescu-Sarkar). They were written following a lecture series given by
Sucharit Sarkar at the Renyi Institute during a special semester on
"Singularities and low-dimensional topology", organised by the Erdos Center.
