How to show italic in vim in iTerm2
You have to update your TERMINFO file.

Thanks to wincent's video and his github pages
Watch the video and look at his github pages, they're excellent.

I have the following note stored on my HD:

We can have italics in the terminal.

This works in iTerm as well as Terminal.

We have to adapt the terminfo database to tell it to display italics.

Create a plain text file which contains the following:

xterm-256color|xterm with 256 colors and italic,
  sitm=\E[3m, ritm=\E[23m,
  use=xterm-256color,


Save it as xterm-256color.terminfo.txt

Then execute the following command:

tic -o ~/.terminfo xterm-256color.terminfo.txt


This will create a ~/.terminfo/some_arbitrary_number/ directory, and inside that directory is a xterm-256color file.

What it does according to the manpage:

       The command tic translates a terminfo file from source format into com-
       piled  format.   The  compiled  format  is  necessary  for use with the
       library routines in ncurses(3X).

       The results are  normally  placed  in  the  system  terminfo  directory
       /usr/share/terminfo.  There are two ways to change this behavior.

       First, you may override the system default by setting the variable TER-
       MINFO in your shell environment to a valid (existing) directory name.

       Secondly, if tic cannot get access to /usr/share/terminfo or your  TER-
       MINFO  directory,  it  looks for the directory $HOME/.terminfo; if that
       directory exists, the entry is placed there.

       Libraries that read terminfo entries are expected to check for  a  TER-
       MINFO  directory first, look at $HOME/.terminfo if TERMINFO is not set,
       and finally look in /usr/share/terminfo.

       -o dir   Write  compiled  entries to given directory.  Overrides the TER-
                MINFO environment variable.


So with the given command we are writing a new terminfo entry in the hidden ~/.terminfo directory. It takes the capabilities of the existing xterm-256color entry (from /usr/share/terminfo/) and adds italics mode to it.  

To check that the terminal does the right thing:


with fish:

echo (tput sitm)'italics' (tput ritm) (tput smso)'standout'(tput rmso)

with bash or zsh:

echo `tput sitm`italics`tput ritm` `tput smso`standout`tput rmso`



I guess at the moment most vim terminal colorschemes don't set italic as a style. To check this do:
:hi Comment if the reply contains cterm=italic you're done.
If not add highlight Comment cterm=italic to your vimrc (below setting your colorscheme).

Addendum for tmux

tmux uses its own terminfo files, they also need to be updated to use italics.  


create a tmux.terminfo.txt file which contains



tmux|tmux terminal multiplexer,
  sitm=\E[3m, ritm=\E[23m,
  smso=\E[7m, rmso=\E[27m,
  use=screen,



create a tmux-256color.terminfo.txt file which contains



tmux-256color|tmux with 256 colors,
  sitm=\E[3m, ritm=\E[23m,
  smso=\E[7m, rmso=\E[27m,
  use=screen-256color,
  

and run the tic command.

tic -o ~/.terminfo tmux-256color.terminfo.txt
and
tic -o ~/.terminfo tmux.terminfo.txt