Chelation
Chelation is used to remove undesirable minerals or compounds from the body.
Kelos is greek for claw and that's literally what a chelating compound does.
EDTA
Ethylene Diamine Tetraacetic Acid (EDTA) is the most famous chelator. EDTA it is the only non-orthomolecular compound Linus Pauling mentions in his book on orthomolecular medicine. He considered it worthy of special attention because is a weak synthetic amino acid (similar to a natural molecule).

EDTA is known as a hexadentate chelator because it can bind using up to 6 (hex) bonds. EDTA has a varying affinity with elements:


The minerals with the lower affinity (Ca/Mg) are replaced with minerals that have a higher affinity (like the heavy metals). EDTA was originally made famous for it's ability to remove heavy metals from the body (especially lead). This is made possible because it has a preference for these heavier metals over the lighter ones.
A large number of medical clinics around the world use chelation to remove calcium plaque from arteries. Chelation has a zero mortality when used correctly N.B. Heart bypass operations have a mortality rate of ~1 %.
Thermography is one way to establish a benefit with EDTA chelation i.e. your extremities will feel warmer (indicating improved circulation). EDTA chelation treatment has the added benefit (over a bypass) of improving circulation to small blood vessels. There are 3 major methods of taking EDTA IV (100 % absorption), rectally (suppositories 90 % absorption) and orally (2-5 % absorption).
Cardiac Calcium Scoring is relatively new but it correlates with heart disease risk much better than other measurements:

NBMI
NBMI (aka OSR1, BDTH2, Emeramide & B9) is relatively new chelator which has a low toxicity. NBMI was originally sold as a food product because it is made by combining benzoate (found in foods like apples and cranberries) and cysteamine (a molecule made by the body) via an amide (-NH-)linkage.NBMI is particularly effective as a mercury chelator because it is fat soluble... and so is mercury. NBMI's two flexible arms make it able to strongly bind elements of many different sizes.
NBMI doesn't deplete levels of essential elements because it only binds with unbound elements (useful elements in the body are all normally bound) i.e. Mercury is fat soluble with 95 % of mercury being found in the fat. The mercury that is measured in the body is the water soluble component... meaning that the bulk of mercury in the body is not being detected. NBMI relies on two sulfur (aka sulfydryl/thiol/-SH) groups to bind the mercury.
Another advantage of NBMI is that it is an extremely strong anti-oxidant with an ORAC (Oxygen Reduction Absorption Capacity) score of 192,400 umTE/100g. This is about 10x stronger than the average anti-oxidant.

DMPS (Di-Mercapto Propane Sulphonic Acid) and DMSA (Di-Mercapto Succinic Acid) are the two existing water soluble chelators. They both have two thiol (-SH) molecules same as NBMI but are only water soluble.
A great explanation of the problem is the case of Karen Wetterhahn a chemistry professor who died from mercury poisoning even though she had no detectable levels of mercury in her blood:

Zeolites
Zeolites are microporous aluminosilicate minerals which have cages that trap heavy metals. These cages are exactly the right size for only certain minerals so they do not remove other desirable minerals. They also trap toxins between layers. Clinoptilalite is the most common zeolite being used and only very small amounts are usually required if the product is one that has been processed.
VitC
Vitamins can be effective chelators: VitC is particularly effective in removing Copper (it is a known copper antagonist).
Selenium
Minerals are often effective chelators. Selenium is good at removing heavy metals such as mercury from the body.