Category template to display child categories

Hi! I’m trying to get a category template to do this:
Display category name & description (done)

Display each child category like this:

<h3>Child Cat</h3>
<p>child cat description</p>
<ul>
<li>Post from child cat</li>
<li>Post from child cat</li>
</ul>

This should repeat for each child of the parent category.

Any ideas?

Thanks for your help!