In which occasions you would like to use italics in web design? Because the use of bold fonts is quite obvious not sure about italics.
From a technical standpoint, you should use italics whenever writing titles of books or films. Things like that.
Italics are used for emphasis. When you want to draw attention to a word. Which is similar to bold, but italics doesn't seem to "jump out" as much. You should never italics a whole paragraph or other huge chunk of text. But you can use it as part of a layout. You could italicize your title, for instance.
Creatively, there's a lot of directions you could go in, in my opinion. But, don't overuse it either.
Here are some resources on topics for italics:
All in all, it's a personal aesthetic decision. If it looks good, keep it. If it doesn't, kill it.