I understand your frustration. We are doing our best to bring more of the features available in the Silverlight interface to the HTML one. Unfortunately, the "group by" mode in the views is one of the things we did not manage to do with the last two releases, but we are definitely going to deliver this functionality later. Stay tuned for future updates and in the meantime you can vote for the "group by" functionality on our feedback portal.
As for now, you can configure the board view so that the items appear grouped by "iteration" or "parent item": check out our documentation for more information about configuring the board view.