• what should their content be ?

Nedjo: Breadcrumbs in Drupal lead up to, but do not include, the current page. Assume a taxonomy like this:

Food (vocabulary id 2)
  grains (root term, id 1)
    wheat (second-level term, id 2)
    rice (second-level term, id 3)
  vegetables (root term, id 4)
    potatoes (second-level term, id 5)
    onions (second-level term, id 6)

When browsing the term 'rice', I assume the breadcrumb should be:

home > food > grains

When browsing a node assigned to rice, the breadcrumb should be:

home > food > grains > rice

We should probably look at the taxonomy_breadcrumb module for comparison.

Frederic: I'm a bit reluctant on this. One the one hand, ISTR that breadcrumbs in drupal are supposed to as you describe. OTOH, there's a snippet to include the page title, which means it is felt as needed and, maybe more importantly, Steve Krug, in its oft-quoted “Don't make me think” book about web usability, insists on including and even boldfacing the last item in the breadcrumbs, and I think this advice is as good as most of the book (I hear even Dries has it). To illustrate this example I'd say that browsing “rice” should give

home > food > grains > rice

and show a page related to the terms rice, typically the list of nodes matching the term. while browsing a node assigned to rice, say Carnaroli, the breadcrumb should be:

home > food > grains > rice > Carnaroli

… which happens to be how drupal works from the home page, which by default displays a node list matching a criterium (published + promoted), from which each node is one level deeper as a detail page. Same with these taxonomy contexts: term page lists nodes, putting the node list in its parental context, and node pages show the nodes, in their parental context.

or possibly

home > food > grains > rice > Carnaroli

to include automatic permalinks within the same logic