Here is what some respected horseman have to say about Natural Horsemanship Training (in their own words):
Tom Dorrance | Monty Roberts | Pat Parelli
Tom Dorrance: 
The part that has meant the most to the horse and me is the communication between us. This is the part where I really had to devote a lot of thought. I have watched horses when they are loose by themselves or loose in a group; gentle raised or wild range raised, their naturalness will show. And by studying their actions and reactions I have been helped to understand how to present myself in such a way that the horses will respond to what I may ask of them. This I believe is true nature. This is something I have had to develop in myself, for myself, by myself. The True Unity and Willing Communication between the horse and me is not something that can be handed to someone, it has to be learned, it has to come from the inside of a person and inside of the horse. See his website for more information tomdorance.com
Monty Roberts:
While tracking wild mustangs in Nevada as a boy, Monty observed a nonverbal communication between the horses, a silent language he would later call “Equus.” Monty incorporates “Equus” into his nonviolent training approach called Join-Up®.
Monty first developed Join-Up® to stop the cycle of violence typically accepted in traditional horse breaking. Convinced there must be a more effective and gentle method, Monty created these consistent set of principles using the horse’s inherent methods of communication and herd behavior. The result is a willing partnership in which the horse’s performance can flourish to its full potential, rather than exist within the boundaries of obedience. These principles are valuable tools to understanding what motivates horse behavior and increasing effectiveness in any application.
Join-Up training methods are most simply expressed in the process of starting raw horses. Without the use of pain or force the trainer persuades a raw horse to accept a saddle, bridle and rider. Working in a round pen, one begins Join-Up® by making large movements and noise as a predator would and begins driving the horse to run away. She then gives the horse the option to flee or Join-Up®. Through body language, the trainer will ask, “Will you pay me the respect due to a herd leader and join and follow me?” The horse will respond with predictable herd behavior: by locking an ear on her, then by licking and chewing and dropping his head in a display of trust. The exchange concludes with the trainer adopting passive body language, turning her back on the horse and without eye contact, invites him to come close. Join-Up occurs when the animal willingly chooses to be with the human and walks toward her accepting her leadership and protection. This process of communication through behavior and body language and mutual concern and respect, can be a valuable tool to strengthen all other work with horses.
Experienced horse people, including Her Majesty Queen Elizabeth II, have called Monty’s method incredible. Two-time, World’s Greatest Horseman winner, Ron Ralls uses Monty’s methods in the foundation for his training work as well. Traditional methods aim to teach the horse to ‘DO AS I SAY’ and involve the use of pain and intimidation, but Monty focuses on communion with the horse, rather than domination. “For centuries, humans have said to horses, ‘You do what I tell you or I’ll hurt you,’ I’m saying that no one has the right to say, ‘you must’ to an animal or to another human,” Monty said.
Join-Up methods rely on horse and trainer establishing a bond of communication and trust. “You must somehow understand that we as horsemen can do very little to teach the horse. What we can do is to create an environment in which he can learn.” Monty says, “We hear that ‘actions speak louder than words,’ but generally we do not live by it too successfully.”
The principles found in Join-Up offer valuable tools for all other work. Riders, trainers, veterinarians, vet techs, farriers, barn managers – virtually anyone handling horses – can use these methods to increase their effectiveness in helping horses fulfill their potential. See his website for more info. http://www.montyroberts.com
April, Pat Parelli, and student (2008)
Pat Parelli:
The Parelli method allows horse lovers at all levels and disciplines to achieve: success without force, partnership without dominance, teamwork without fear, willingness without intimidation, and harmony without coercion.
Founded in 1981 by lifelong horseman and teacher Pat Parelli, the Parelli Program combines common sense psychology and communication. Unlike many training programs, the Parelli method teaches the human, not the horse. Early on, Pat realized that horses already had all the skills they needed to thrive and relate with their kind. It was adding the human element that complicated things.
Horse owners who follow the Parelli program have found the greatest gift is discovering that Parelli enhances not only their relationship and communication with the horse, but touches every other relationship in their lives.
“It’s more than just about the horse,” reflects Linda. “It really dips into the personal development side of things. You learn about yourself, you learn about communication, about leadership, about truthfulness, about consequence and responsibility. You learn about love and imagination. The horse becomes the animal that tells you the truth about yourself in all these categories.”
“People realize this is what they’ve been looking for in all their relationships,” adds Pat. “It’s balanced with love, language and leadership in equal doses. The program and their horse give them a living model so they can practice and become fluent in their abilities in all relationships, not just the horse relationships. See the Parelli website for more information.http://www.parellinaturalhorsetraining.com/.