Headless machines need a head somewhere. A barebones text terminal run via a serial port is the base option. A remote graphics desktop gets into the virtual machine and full access territory. Faster networks and more capable computers and graphics have made the full desktop option feasible enough that Raspbian takes very little to set it up. How to Set Up Easy Remote Desktop Access in Linux by Jack Wallen gets into the Ubuntu and Fedora situation and explains a few things that help fill in the current state of the technology.
Linux is a remarkably flexible operating system. One of the easiest means of understanding that is when you see that, given a task, there are always multiple paths to success. This is perfectly illustrated when you find the need to display a remote desktop on a local machine. You could go with RDP, VNC, SSH, or even a third-party option. Generally speaking, your desktop will determine the route you take, but some options are far easier than others. Once you understand how streamlined modern desktops have made this task, your remote administration of Linux desktops and servers (with GUIs) becomes much simplified.
Here’s the Raspberry Pi documentation on Virtual Network Computing.
Sometimes it is not convenient to work directly on the Raspberry Pi. Maybe you would like to work on it from another device by remote control.
VNC is a graphical desktop sharing system that allows you to remotely control the desktop interface of one computer (running VNC Server) from another computer or mobile device (running VNC Viewer). VNC Viewer transmits the keyboard and either mouse or touch events to VNC Server, and receives updates to the screen in return.
This one also has step by step instruction based on the Real VNC software. Here’s Instructable’s Setting Up a VNC Server on Your Raspberry Pi and at Adafruit, too.
As Wallen notes, there are a number of options and you can find more about them by a bit of research. Here’s a discussion on the Raspberry forums about the best VNC server to use. It’s another technology where you can experiment to see how it works without too much trouble or expense.