How to list the latest 3 entries per category per section? I'm trying to create a condensed overview of my website content on my homepage. I'd like that page to loop through all sections, in each section looping through the categories that apply to the section, and for each category to pull the title, uri, and excerpt of the newest three entries.

I'm having trouble wrapping my head around how I'd do that.

What I'm after might be seen as:


SECTION
  CATEGORY 1 [title, description, view category archive]
    POST 1 [title, excerpt, publication date, view entry]
    POST 2 [title, excerpt, publication date, view entry]
    POST 3 [title, excerpt, publication date, view entry]
  CATEGORY 2 [title, description, view category archive]
    POST 1 [title, excerpt, publication date, view entry]
    POST 2 [title, excerpt, publication date, view entry]
    POST 3 [title, excerpt, publication date, view entry]
SECTION 2
  CATEGORY 1 [title, description, view category archive]
    POST 1 [title, excerpt, publication date, view entry]
    POST 2 [title, excerpt, publication date, view entry]
    POST 3 [title, excerpt, publication date, view entry]

For the sake of simplicity, all my categories are currently under a 'global' group. They also map pretty much 1:1 to the EntryTypes available in each section. (I'm not entirely convinced I'm using Categories / EntryTypes correctly, given that 1:1 relation... in fact that's another question to ask).
You need to loop over the sections. In each section, you then loop over the categories, and display your entries inside them. Something like this.

{% set categories = craft.categories.group('groupHandle').find() %}
{% for section in craft.sections.getAllSections() %}
    {% if section.type == 'channel' %}
        &lt;h1&gt;{{ section.name }}&lt;/h1&gt;
        {% for category in categories %}
            &lt;h2&gt;{{ category.title }}&lt;/h2&gt;
            {% for entry in craft.entries.section(section).relatedTo(category).limit(3).find() %}
                &lt;a href="{{ entry.url }}"&gt;{{ entry.title }}&lt;/a&gt;
            {% endfor %}
        {% endfor %}
    {% endif %}
{% endfor %}


This is a pretty quick and dirty example. I pull the categories ahead of time so I can reduce the number of database calls. I suggest using the cache to speed things up.

The template docs (especially the ElementCriteriaModel) are handy reading materials.