The martingale collar can be a useful tool but it is not a training tool. For that matter there are very few tools I would say are training aids.
Is the martingale collar right for you?
If you have a large dog that you are struggling to maintain control of. However, I would rather you just train the dog using a harness and if necessary a halter (head collar). A martingale collar can offer temporary relief to leash pulling but don't delay training!
Aggressive dogs who can snap unpredictably and you are putting them in situations where the risk of an aggressive outburst is possible. This shouldn't be done without guidance from a behavior expert and lots of other management tools should be in place. (The collar is not for training but to make sure you can quickly and effectively control the dog in more risky situations if it becomes necessary to do so.)
Dogs that have learned to slip out of their collars or are fearful run a risk of bulking. Again the collar is not going to help train the dog out of fear responses but it is a necessary tool to keep the dog from slipping away and darting into traffic.
I recommend that a martingale be used in conjunction with a body harness and as a secondary system if things get complicated. It should not be the first or only equipment being used.
Warning: Do not leave a martingale collar on a dog when not attached to a leash. This is specifically and most importantly true for prong/pinch collars.
Speak with your behavior consultant before deciding if a martingale collar is an appropriate tool for you and your dog.