Though there have always been working dogs (even the earliest domesticated dogs performed some functions, usually guarding camps or performing clean-up duties of rubbish and waste) dog training as we know it today really started in and after WWII.
Thousands of dogs were recruited and trained for World War II, kicking off the Dogs for Defense program that's still used by the US Military to this day. After the war, veterans returned home to their families, which now frequently included pet dogs, because this was the 50's.
At this time in the United States, the military had the most vast knowledge of dogs and dog training, and it made sense that former military men would have been the dog trainers of choice. Many formal obedience training techniques are based in military styles and drills of training; even some of the language such as "boot camp" sticks around in the dog training lexicon to this day.
Some of the harsh, get-it-done, choke-chain and hanging training methods filtering out of military training may not have been the *most* appropriate for the average little household Cockapoo, but that was the only training option those dogs (and their owners) had.
A couple of decades passed. In the 80's, there were some studies of wolves that seemed to indicate that dogs were basically wolves, and training methods should switch over to a pack-based, dominance-based, hierarchy-based method. Since most of the obedience training methods used physical compulsion and painful corrections, this fit right into the pack theory of the 80's.
Another decade went by, and there began to be a lot of buzz and commotion from Southern California. Trained sea mammals were appearing at places like Sea World, and some of those dolphin and whale trainers were also working with other species, namely, dogs. Dolphins and whales obviously could not be trained through compulsion (force) and instead they had developed a reward-based, motivational system involving mysterious-sounding training techniques like shaping and capturing. A "conditioned reinforcer" (whistles for dolphins, clickers for dogs) was used, and what a powerful training tool it was!
The more progressive trainers "crossed over" from the old-fashioned, compulsory-based training methods to the newer, more dog-friendly ones throughout the 90's. (I was a relatively late bloomer, handing in my choke chain/strangle collar in 2003.) These days, the vast majority of trainers use the humane and dog-friendly methods developed in the 80's and 90's, and these are the methods officially recommended by the American Humane Society and the American Veterinary Association as well as most other animal care groups and associations.
So where are we now, in this "brief history of dog training?"
One current trend is the use of more and more science, research and documentation in training. Have you ever heard a trainer say "This method always works" or "This method works best?" A current trend is to find the scientific analysis of those kinds of statements to ensure that they are actually valid. For example, "Playing tug with your dog causes aggression." This was actually found to be untrue; playing tug with dogs has NO scientific correlation with aggression. On the other hand, owners who reported playing any type of game including tug with their dog reported LESS aggression. Scientific research for pet dogs has never been very common or popular, but hopefully the field will grow.
Isn't that interesting! It's a fine time in history to train your dog!