st currently does not keep any mode for the cursor that was active
in the underlying glyph (e.g. italic text), the mode is always
ATTR_NULL [1].  At [2] you can find a screenshot that shows the
implications.  Other terminals (at least vte-based, such as
XFCE-terminal) keep some modes for the cursor.  I find the current
behaviour very disruptive, so here is a patch that keeps a few
(arbitrarily chosen) modes for the cursor.

[1] http://git.suckless.org/st/tree/st.c#n3963
[2] http://i.imgur.com/R2yCEaC.png

This is used by, e.g., tmux.