You can find the features that Cosmos offers at Features. Many users have produced demos that use basic networking and graphics, but the core team is still focused on kernel and debugger. When we have the foundation built to a sufficient level the core team will integrate the work of users into Cosmos itself.
To answer your question, Cosmos currently has a VMware SVGA driver (up to 1920×1200, but only works on VMware platforms), a VESA-BIOS-Extensions (VBE) driver, and a non-working-at-the-moment VGA driver (up to 320×200, such wow!). A Cosmos Graphics Subsystem (CGS) is in development, offering basic functions for drawing shapes under any graphics driver. CGS currently works on VMWare, Bochs and VirtualBox (and any other hypervizor that uses VBE graphics!)
Basic networking is being worked on, and the FAT filesystem driver works but has very few bugs.