I was a picky eater as a child and it turned into a HUGE DEAL because my parents would try to insist that I finished my dinner every time. I was stubborn as hell so I dug my heels in, but it also made me anxious around mealtimes (feeling like everyone was watching me and pressuring me) which made me lose my appetite. I had definite texture issues (hated 'slimy' food and liked crunchy food, still do) but left to my own devices I would have had a fairly repetitive but not unhealthy diet. (I could have eaten pasta with tinned tuna, peas and broccoli with apple pie to follow for dinner every day, which is not that unreasonable in terms of nutrients, really.) We had huge fights that usually ended in me crying, even when I was nine or ten which is way too old to burst into tears over dinner.
I only really grew out of it when I left home and could choose to eat exactly what I wanted when I wanted. I absolutely had a short period of eating everything I was never allowed at home, from Haribo to Ribena to Nutella, but that settled down quite quickly. I'm still suspicious of new foods initially but am much more willing to try things now it's my idea.
My advice is really the same as everyone else in this thread.
1. Cook dinner.
2. Place dinner in front of child.
3. Eat your dinner (or do something else like clean the kitchen if you're eating at a different time. Don't just sit there and watch them.)
4. Clear up.
What your child does or does not eat during step 3 is none of your business. Don't discuss it. Make a huge effort to just not care while you're sat at the table. It's kind in step 1 to choose some foods they definitely like from time to time, and to pay attention to the sorts of things they like (do they also go for raw vegetables? Is anything OK when it's covered in cheese sauce?) but if you make an effort to offer variety it won't be crucial. If they are hungry later, I would allow them a snack if it's been a few hours, but I would make it the exact same boring snack every single time - like a bit of apple or a piece of mild cheese - whatever they'll eat but don't especially like. If they're hungry they'll go for it, but snacks don't mean treats. I think getting out leftovers again is mean - I wouldn't do that.
And pick a length of time to do this for. I would say no snacks for the first 48 hours, and you have to stick to your guns completely about just giving them dinner and ignoring them eating it for a month. If you're still having huge problems at that time and have seen no improvement, see a doctor in case it is a health issue. I reckon as a very stubborn and anxious picky eater it might have taken me up to a week to crack if my parents had done this totally consistently. Maybe two days to really feel the hunger, and then a few more days for the "eating is stressful" anxiety to subside. But any child will crack eventually. You might feel worried about them, but it's your worry vs their hunger. Total consistency is the key.
People talk about food being a control issue for a child, and them trying to provoke a reaction, but I think they forget that such conscious thoughts are not what is going through your child's mind. They're not doing it on purpose but it's a subconscious feedback loop which you are enabling - either positively, that not eating gets them control and attention, or negatively, that eating is associated with anxiety and so it's difficult. Break the cycle.