Note: The "live", dynamic, nature of Excel charts can not be maintained in Illustrator. What pastes is non-dynamic - meaning you can't easily alter the data in any chart pasted into Illustrator from Excel. Charts paste as artwork not as live charts in Illustrator.
The charts don't always paste wonderfully "as is". You need to some minor clean up at times.
Using an Excel Chart:
Simply copy, switch to Illustrator, and Paste:
You'll notice the chart pastes with a rectangle around it to indicate the "chart area" in Excel. These are clipping masks in Illustrator. So you need to remove them.
(The type reformatting is due to Excel formulas and is another matter. I'm merely using a downloadable template from the web here and generally I replace any text, so I, personally, never concern myself with the type issue.)
So, switch to Outline Mode (
View > Outline).
Then select and delete the rectangles:
Switch back to Preview Mode (
View > Preview) and you'll find vector paths and elements you can easily alter:
It's the same for Box and Whisker charts... they paste with clipping masks (rectangles).
Just remove the clipping masks to easily access the actual artwork:
(Note: Using Excel 14.7.2 and Illustrator CS6 here - it can only be better in more recent versions.)