Here is a short summary of it:
The gustatory perception (taste) of anything sweet triggers a release of insulin into your bloodstream because your body thinks it needs to deal with sugar. Since there is no sugar to be dealt with, the insulin released causes increased fatty acid synthesis, causing fat cells to take in blood lipids, creating triglycerides. High levels of triglycerides in the bloodstream can cause atherosclerosis as well as increased risk of heart disease and stroke.
Furthermore and in general, drinking diet sodas or using an artificial sweetener is far worse for your body than drinking a regular soda or using natural sweeteners, like sucrose. Most artificially sweetened products contain aspartame to give it a sweet taste. When ingested, aspartame breaks down into various other compounds including Methanol and Formaldehyde
Yup, nothing that tastes good is good for us. I personally can not drink artificial sweeteners due to getting an immediate migraine; same for anything with MSG in it. I can't stand to drink just pure water either, tea is my choice.
To be even more open...I eat pizza or a pizza like sub 4-5 days a week. I was still able to lose weight with this stuff and continue to eat the same. However I have always been an athletic build with probably pretty high metabolism. Pizzas can be made "bad" but overall it is not too bad if you know what you are doing.