The term "Dobsonian" really applies to a style of mount rather than a telescope design. The "Dob", was developed by John Dobson, and is merely an extra-large Alt-Az mount with the capacity to hold a very large Newtonian reflector.
Dobs are available from nearly every telescope manufacturer. They are also found at star parties in prolific quantities as homemade instruments, in sizes ranging from small to ridiculous. Orion offers their SkyQuest XT4.5 Classic Dob in a 4½” diameter for $219.95. On the other end of the scale... well, we have an enormous 42-incher dominating the middle of our showroom.
A major advantage with a Dobsonian is that there’s apparently no limit on aperture size. If you have the room to store the components, and the means to transport them, then you qualify as a big-Dob owner. Another major advantage is – it won’t take much loot to get one.
Standard Dobsonians don’t come with setting circles or slow motion controls, so positioning them is strictly a manual-labor arrangement. However, since that situation is more than most are willing to put up with, many Dobs are at the very least equipped with after-market encoders and digital readouts to aid in finding objects. Then too, there is the more sophisticated option of a motorized GOTO system that can find objects, track them flawlessly, and adapt perfectly to astrophotography.
There are companies that manufacture large-aperture turnkey GOTO systems which work extremely well, and can cost as much as a used car. We've had some chances to sit at the controls of some of these grand behemoths. We were always very pleased and impressed. But pricewise they are light-years beyond our reach.