The top tabs, left navigation and breadcrumbs are all built on the ASP.NET Navigation API. This uses a provider architecture - providers give you the model (Tree of SiteMapNodes) for the site, and navigation controls, such as the SiteMapPath web control (used for breadcrumbs in SP2007), which render that model in a way the user can use.
SharePoint ships with it's own controls for both parts - providing models and display - though it also uses standard ASP ones.
Probably your best bet is to check the web.config for your web application - this will have section in it that details the navigation providers that SharePoint comes with preconfigured in the section. The names of these providers will be shown in your pages as data sources for your navigation controls.
If you're using Enterprise, the big thing to note is that some of the navigation providers will use the publishing features. To support publishing pages, these display quite a different model - but that model can include Publishing pages and is generally a bit easier to configure to display a useful navigation structure dynamically. It does, however, lack some of the features of the 'normal' team site navigation, such as the Portal Site Map connection.
You can add your own configurations of the providers to Web.config, but be sure to do it via an SPWebConfigModification.
You can also control how your navigation appears by controlling things like if the left or top navigation shows 'fly out' menus, what's shown in the breadcrumbs, etc.. To make these changes, you'd probably create a new master page, or possibly change your specific ASPX page for your site.
Finally, you can write your own navigation providers (or new providers, if you write one), or navigation controls. It doesn't necessarily have to be a complicated thing to do, and can be quite useful! I did one for a case management system a while back that provided 'related cases', and this was convenient as I could easily plug it into existing navigation controls to display it consistently with other navigation in the site.
You may find this useful: http://www.novolocus.com/tag/navigation/