Bookmarks work, but I find them cumbersome. The outdated part for me is having to put them into folders manually, which doesn't have the best interfaces for this. I think that's why so many people load so many tabs at once, if you close the window getting them back is difficult unless you want to hand-sort hundreds of tabs in some cases.
I'd like to see them stored in a database where you can get the data out by running filters. Those filters should be able to search meta data about currently opened tabs, browser history, saved tabs or sets of tabs, and some data from the web pages themselves. It should be simple to search all my currently opened tabs for a list of terms (like sql, select, from, where, etc) and have them be moved from my current window to a new window. I should be able to save these as a set of tabs labeled "sql". If that set already exists, it should combine them, throwing out duplicates. Ideally, web browsers should have the ability to save keywords from pages you have visited in your own little web data store. If I ran across a reference to a particular subject in the past few days, I should be able to search my history and my store of keywords for pages that mention that subject, and load them all into a new window that can be saved as a set of tabs. I should be able to search for web pages in a set of sets of tabs that have been modified in the last hour. Or open all images I've seen on webpages in the last couple of days or that have a keyword in the image name.
Manually sorting bookmarks does work, but I'd like to see something a lot more robust. I can, for example, bring up the history sidebar and see if I can figure out which site I was on that mentioned a particular game or physics term or whatever, but it should be a lot easier to do these things. In Firefox I can search page titles for a specific page, but it won't search through the page contents.
On a related note, it seems to me that all browsers should be able to act as web spiders so that every page you come across through daily operation goes into your own search terms database and that searches should start there before going to one of the search providers. Maybe have them spider links on each page a level or two down so you can find related items easier even if you didn't actually go to the page in question. You would also be able to search the parts of walled gardens you've visited lately, which normal web search won't see.
Anyway, I'm just spit-balling here, but it seems like there is a lot of room for innovation in how we select, save, group, and access web pages.