The brushes for Photoshop and PS Elements are in ABR. Not all the sets on the graphicxtras site are in ABR but many of the sets contain the ABR. The ABR has been around for a while but the format often changes and if you use Photoshop CC 2014 then you might find that you cannot open the really early ABRs. Likewise, if you save an ABR in Adobe PS CC 2014 and then try and use that in an earlier version, it will probably be rejected. The ABR cannot be read by most applications though you should be able to find some, they are listed below.
Many of our sets also include the brushes in PNG. They can be turned into standard Photoshop brushes ABR by define brushes command in the edit menu. Many of the sets on the site also includes an action which can run through all the PNG images to add them to the brushes panel. You can then just go to the right side menu and save the Photoshop brushes to a new ABR (in the current version of Photoshop)
You can find a conversion tool called ABRMate, you may find it useful but I can give no recommendations as I have not used it. If you want to convert, browse etc brushes then it might be a very useful tool to add to your collection of software applications
There used to be a document giving the details of the brushes format and if you search for 'Photoshop brushes specification' then you might find a PDF or html document relating to this. It is quite likely that any specification is fairly old now and the latest specification is very different. The format is a propriety format and is probably regularly updated by Adobe Software Incorporated. A cursory look into the specification suggests the brushes are a resource of 8BIM. Most of the information is in binary and at the end of the ABR there are some details about the names of the brushes along with details about using the color dynamics, dual brushes, use pose, use tip dynamics, size etc. Certain people with more understanding of this will be able to make much more of the format
Not certain if they work with the current OSes or how effective they are with all formats of ABR
Photoshop and PS Elements are not the only applications that support ABRes, you can load them via Postworkshop Pro as well as GIMP and PSP. The applications do depend on the version of the ABR so not all formats can be read.
The ABRes are totally cross platform and can be used across platforms: PC or MAC OS X. So yes, you can use that stunning Photoshop brushes on your PC as well as your mac. Simply copy the ABR over to your other machine (the license for the use of the brushes allow you to use the brushes on any number of machines as long as it is based on the individual and not for an entire firm of networked users. There is no conversion required, they work exactly the same way.
Who knows ? I am the worst person in the world to speculate on what features will be added to the ABRes specification in the future. I would love to see it have a lot more brush options such as including blurring, smearing, color bleeding, noise, glow features, animation, etc smart brushes for all kinds of projects. The ability to brainstorm a whole range of brush strokes would be nice. Perhaps the format could also include a blending of more than just two brushes ? The ability to change a brush in the brushes panel and all the brush strokes in the design, change (a linked brush option ?) Certain the developers of the brushes format will surprise us at some point in the future. The key thing for me is that the format is still accessible but that is forever changing. The recent changes to the brushes specification have been subtle and I would love to see another leap forward in brush technology in 2015, 2016 etc.