training collars

I believe those collars are called Martingale Collars and from what I have heard from member they dont actually choke the dogs like a regular choker would. As for your dog using one, if hes doing fine without one I really dont see a need to use it.
 
Here is a pic of a Martingale Collar:
 

Yes, thats it! Tootsie is not a puller and well behaved on a leash,so I'm not quite sure if she needs it or not. The dogs wearing them are well behaved, so I don't see or understand the use for them.

As far as I know there are two purposes to them - first understand that the way they work is to tighten only a bit (not unlimited like a choke chain). So, some people use them for dogs who tend to slip their collars. Any attempt to pull on the collar or any tugs on the leash would make this collar a bit tighter, not looser like a regular flat collar. And then I think some people use them to discourage pulling with a little neck pressure more safely than one would with a choker... not sure if leash pops are issued with these too.

Our trainer recommend the Martingale, so I just bought one for both dogs. I've put them on, but I'm not really sure how to use it so I haven't walked them on it yet. I know it won't hurt them like a choke collar, but I'm still a little nervous about using it wrong and hurting their necks.
 
I think you're right though, Jones. People do use them so the dog can't slip their head out. It seems like it might be a good tool for teaching loose leash walking, if I knew how to use it correctly.

Hmmm..... She has slipped her collar a few times and her harness doesn't fit that well. Maybe this collar would be good. Is it only used for leash walking?

The Martingale collars were originally made for sighthounds only, as they couldn't be trusted on a flat collar, but chockers and pinch collars were too much for sensitive skin.
 
Sighthounds as a whole generally don't need harsh corrections, and so the martingale (also called a half check or limited choke) was made for them.  The pictures you've seen are not of true martingales, but rather those made for commercial use by others. 
 
Sighthound martingales are generally much larger width wise, and cover a good deal of surface area on the neck.  They are not a true training collar, and few people "pop" a dog on a martingale. For dogs that are handler sensitive, the martingale is a good way to have contact with your dog and allows the dog to know what's going on

Not that I'm advocating leaving a dog tied up, but our trainer said she will use it if she has to leave her dog somewhere for a minute, because if they pull they cannot get out of it. I wouldn't really use it for anything but leash walking, because it doesn't "break away" like a normal collar if they're playing or get it caught on something.

As of 2 weeks ago my 27 month old Eskimo has a Martingale.  We started to take specific issues training - in short, his original training was treat based so with a very smart and very stubborn dog I had to do something.  This trainer uses the Barbara Woodhouse method - and I am old enough to know that meant choke chains.  She starts dogs off with the choke and then they usually move up to a Martingale or a flat collar.  Our Eskie has 3 Safety Harnesses in good shape so he will be keeping those and not getting a rolled leather collar.  My dog does not like the choke and I do it as I am afraid I will not correct properly, so bought the Martingale - a Canine Equipment "Ultimate" - nice and cushiony.  My dog is a puller, no doubt about it, but I also have a NewTrix which he hates and I frankly don't use - but I wanted him to learn to walk and ignore other dogs barking at him - basic manners - and to Sit, Down, Place etc. without having to give him a cookie as a reward.  Have to tell you in 2 weeks his has improved beyond belief.  He doesn't hate the Martingale to extent he hates the choke (which I carry around my wrist as a reminder).  The little devil will flatten himself as soon as he sees a cookie, but when we practice with the Martingale he will divert his eyes - so stubborn - so we keep at it.  If I have the chain section at say 8:00 and pull slightly down on it he will very begrudingly go Down so he does know the word.  But he is walking much better and will set at curbs - although often he will turn and face the houses rather than the street - his way of telling me where to shove it no doubt.  I am way more comfortable with Martingale as well as it is impossible (unless you are my husband) to put it on incorrectly.  With the choke, it has to be as a "P" not a "Q" - I always tested on my wrist - husband didn't and my Eskie has a really thick double ruff of fur.  So Martingale goes on one way.  But "dear" husband took him for a walk just before he left Sat. for a business trip - and for the first time I didn't detach leash from collar before going out - pulled it over pup's head as he does - and off we went.  He was more inclined to eat grass behind me and suddently I felt nothing - in panic I looked and sure enough collar was off, car was coming and a squirrel was about to run into road with my dog after it - I grabbed his fur - so happy for once he has so much of it and flattened myself over him - then examined the leash/collar.  There are 4 hooks - the 3 that work the tightening of the metal - and a fourth that is on the fabric portion just as on a regular collar - that is where he had attached it so collar was really big.  My heart is still pounding.  Other than that, I am comfortable with collar - but it is used only for his walks - never left on at home or when he goes to his weekly socialization.  In car he wears his harness and then I put on Martingale when we get out.  Some of his short haired friends at socialization wear the Martingales all the time - of course they are supervised - but you can readily see if there is a problem. With my guy you wouldn't be able to and all of the dogs like to play with his tantalizing tail - one holds him in a headlock - so have to be careful.