Dumog is the term used in Eskrima to refer to wrestling techniques. A specific system of Filipino wrestling, Buno, is considered by some to be more advanced. "Combat Judo" is another local name. Buno is the term typically used in Luzon, specifically in the Southern Tagalog provinces as far south as Mindoro while Dumog is the term more widely used in the Visayas and Mindanao.
In general, dumog is a basic Filipino technique that is often taught along with Silat, Kali, and Arnis styles. A dumog technique encompasses a variety of pushes, pulls, weight shifts and joint locks designed to "move" the opponent. It is a term used to describe a technique that creates a quick change in weight or force which is very similar to the soft styles of martial arts such Aikido.
The core of the technique is to utilize your own and the attacker's own body weight to force them to try to regain their balance. An example of this sort of dumog could be seen by a fighter defending himself from an attacker trying to clinch (like a Muay Thai style clinch). The fighter would grab his other arm inside the joint of an opponent attempting to clinch him and drop his weight downward immediately. The sudden shift of weight forces the opponent to temporarily be pulled forward which could potentially expose an opening for a counterattack such as a headbutt or even another dumog technique to push their weight back as they attempt to correct themselves.
These techniques can often be performed just as easily with a weapon such as a sword or an eskrima stick, e.g. replace grabbing one's own arm with grabbing the other end of an eskrima stick.)
The term "dumog" is also used in the Philippines to describe dogs, kids or drunk people wrestling around without any skill (brawling).