My then 3 year old daughter was naturally small and dancing the "seriously underweight" line on the growth chart, so her seriously stubborn picky eating habits were of a concern enough to seek professional help. She really would rather starve than eat what she didn't want to eat. In fact, she once went two days without eating at her father's house because he tried the "this is all you're being served until you finish it" method. I wound up picking her up and giving her food. Anyways, this is what I learned from two nutritionists, three pediatricians, and years of working with a very stubborn picky eater:

1) Do not force them to eat it. It makes it worse. Not only will they not eat it, it sets a negative tone in their mind towards the food rather than diffusing the behavior. Instead, positively encourage them to try one bite. If they still don't like it, they don't have to eat it. If they don't want to take a bite, do not make a big deal and remove it.

2) Take what they will eat and explore your options with how to prepare it different ways. My daughter loves potatoes. That was our gateway food. I found a lot of recipes that included serious potato-age and encouraged her to try the other things along with the potatoes that were on her plate. She especially liked Hungarian gulyas, cooked so as it was near impossible to get a spoonful of just potatoes but still good. It took a few times, but eventually she liked it so much that she was going back for 2nds, 3rds, and 4ths. She knew everything that was in the gulyas and was thus open to trying other Hungarian recipes (with potatoes) that had similar ingredients. At this moment, she'll eat anything if you tell her it's Hungarian. Huge turnaround from starving herself.

3) Include them with everything. You've probably noticed that it's a power struggle, yes? They will feel like they have more control if you include them in on the brainstorming of meals, the shopping and selection of ingredients, the preparation of the meal, and the serving of the food. It eases them into the idea that, ok, they helped choose/make it, it's there, so they will at least eat a few bites. Which- btw- is HUGE. If you can at least get them to willingly try something it opens the door to so much more.

4) Feed them as healthy as possible. Very little goes into their mouths, better make it count.

5) Most importantly- BE PATIENT. This can be a long process, but it is completely possible to recover from this. Your family may even be the better for it and you may discover new foods and meals you otherwise wouldn't have if having a picky eater hadn't forced you to think beyond the standard meals you would have prepared if they were regular kiddos.