The Browser Object Model provides access to information about the address of the current page by reading from the location object and you can change the page either by updating the location or by selecting a different entry from the history.
More Cross Browser Options
Most of the other elements that the browsers have all implemented consistently are of less use. The options for opening, closing, resizing, and moving windows will only work if your visitor allows it. You can find out what the size of your visitor's screen is but that is only useful in connection with performing window manipulations since it has no relevance to anything inside the browser viewport.
The least useful of the BOM elements that is reasonably consistently implemented is the navigator element. Those properties which are consistently implemented are under your visitor's control and those which are not under your visitor's control are not consistently implemented.
Build Your Own
The lack of BOM standards means that the most useful information about the browser is presented in different ways in different browsers. We therefore need to build our own cross browser methods to look up the browser viewport size, current mouse position and page scroll position that gets the information from whichever of the different places that the various browsers provide that information in.
An efficient way to add all this functionality in one go is to use my dollarB object which has cross browser properties for viewport size and scroll position and methods for mouse position.