Much of the current trend is down to studies carried out in the 1950s on wolves in captivity - what we know now, but didn't then, is that the study was fatally flawed in two ways. Firstly the dogs were captive, so not behaving as they would in their natural environment, secondly the group was made up of random individuals rather than the family members that typically make up a pack. The end result is that the picture obtained, one which has been widely used in the last 50 years of dog training, was a false one. In fact modern scientific research has effectively debunked the theory that it is necessary to dominate a dog when training it.
Below are links to a sample of resources that provide scientific references and/or useful commentary on the subject.
American Veterinary Society of Animal Behavior Position Statement
International Positive Dog Trainers Association article
NY Times Article about the Cesar Milan approach with quotes from wolf expert David Mech
Publications by wolf expert David Mech
Watch the "Alpha Roll" in action
DOGS: A NEW UNDERSTANDING OF CANINE ORIGIN, BEHAVIOR, AND EVOLUTION
by Raymond & Lorna Coppinger.
Biologic Basis of Behavior of Domestic Dog Breeds by Roy Coppinger and Lorna Coppinger
Here is an excerpt from the above:
Interviewer: Among your new views of the dog is a rejection of the trainer as the "alpha wolf" and the dogs as the "submissive pack member." Why have you rejected what has essentially become dogma in the dog training world?
Ray and Lorna: The alpha wolf model of dog training certainly does appear frequently in print, but we wonder if it was ever really incorporated into serious dog training. We suspect it was never very useful in training dogs, and that almost everybody intuitively knew that. It was "say one thing, do another."
Certainly all the new techniques, such as click and treat, are not based on dominance. We've watched top trainers like Terry Ryan and Ken McCort, and never saw any hint of "I'm the dominant wolf." People who try modifying aggressive dogs don't try to "dominate" them into submission. Everybody agrees that would be a disaster. Imagine training a wolf by dominating it. Quick way to get killed.
It is a mistake to think that because dogs are descended from wolves, they behave like wolves. Wolves do not show the "alpha roll," or any other hierarchical behavior, except in specific circumstances, particularly during reproductive and feeding behaviors. Wolf packs on a hunt are working cooperatively, and hierarchy goes by the board.
Training dogs is fun for me and for the dog, as it should be. Our sled dogs ran because running is fun and feels good. Endorphins are released, social interactions are increased. Try running while you're being submissive. Dogs aren't pulling sleds because they are forced to or are submitting to some person's will. Everybody who ever drove dogs knows that you absolutely cannot force them to do it.
Interviewer:It will be hard to get that alpha wolf/submissive wolf thinking eliminated from the parlance of dog training, but for starters, how should people think about their relationship with their dog?
Ray and Lorna: It won't be hard to get the wolf pack mentality to go by the board simply because we don't think many of the experts ever really believed it. It is through social play behavior that animals learn from one another. Further, it is fun to play with our dogs even if none of us learn anything. It will certainly make more sense to the dog than to be tumbled onto its back and growled at by a human.
Colin Allen and Marc Bekoff have recently drawn attention to a category of behaviors they call intentional icons. Dogs have signals they use when they want to play — the play bow. The play bow is a signal that all the following behaviors like growls and snarls are all in fun. Consider what might happen if you gave the "dominant male" intentional icon, indicating everything that happens from now on is about the driver being the dominant dog. The sled dogs, if they were reacting as submissive wolves, would then lie on their backs and pee in the air instead of running as a team.
Instead of threatening our dogs every time we want to train them, we need to perfect the human play bow which tells the dog the games are about to begin. Remember that games have rules, and what the dog and the humans learn during play is what the rules of the game are. That makes sense in teaching or training, whether it is dogs or students. The intent of dominance display is to exclude the subordinate from some activity, like breeding. The alpha wolf isn't trying to teach the subordinate anything.