Alitame is a non-nutritive sweetener and artificial sweetener approved for use in Australia, New Zealand, Mexico, China, & the EU, but does not have FDA approval – meaning it can’t be used in the United States. The name alitame comes from its chemical formula, which includes a “dipeptide of L-aspartic acid and D-alanine, with a terminal N-substituted tetramethylthietanyl-amine moiety.”  While aspartame consists of the amino acids aspartic acid and phenylalanine alitame consists of aspartic acid and alanine, thus the naming convention alitame. The other dipeptide that derives from aspartame is neotame, which became the newest FDA-approved artificial sweetener in 2002. Alitame is older than neotame, dating back to its discovery in 1979 by chemists at the Pfizer pharmaceutical company.
A U.S. patent covering branched amides of aspartyl D-amino acid dipeptides was granted in 1983.  Pfizer filed a petition with the FDA in 1986 seeking approval for alitame as a food additive. For reasons unknown, the FDA never took action to approve the sweetener. As of June 12, 2008 Danisco – the company that now owns the patent – has withdrawn it’s request for FDA approval, citing “uneconomic production.” 
Some of the benefits of alitame over aspartame include the ability for people with phenylketonuria to consume it. Phenylketonuria, a rare hereditary disease, is found in people who don’t have the enzyme to break down phenylalanin (a form of phenylalanine) in the body, which is a component of aspartame but not alitame. Alitame is also more stable under hot or acidic conditions (but less stable than saccharin or acesulfame potassium). Lastly, alitame is listed as being 2,000 times sweeter than sucrose, which is 10 times sweeter than aspartame. However, neotame is approximately four to six times sweeter than alitame.
Alitame is known to have “a clean, sweet taste.”  “From an oral load of alitame, 7-22% is unabsorbed and excreted in the feces. The remainder is hydrolyzed to aspartic acid and alanine amide. The aspartic acid is metabolized normally, and the alanine amide is excreted in the urine as a sulfoxide isomer, sulfone or conjugated with glucoronic acid.”  Essentially, this is telling us that alitame is not hazardous and goes through normal processes in the body, even though it is metabolized to some degree.
In Europe, it is known as E956. Alitame is also sold under the brand name Aclame. It is “used in a wide range of foods and beverages, including bakery wares, water-based flavored drinks, dairy-based drinks, dairy-based desserts, cream, edible ices, jams, confectionery and some dietetic foods.” 
For avid chemists out there the true chemical process of alitame is as follows:
Alitame is prepared by a multistep synthesis involving the reaction between two intermediates, (S)-[2,5-dioxo-(4-thiazolidine)] acetic acid and (R)-2-aminoN-(2,2,4,4-tetramethyl-3-thietanyl)propanamide. The final product is isolated and purified through crystallization of an alitame / 4-methylbenzenesulfonic acid adduct followed by additional purification steps, and finally recrystallization from water as the 2.5 hydrate. 
Here is a study using alitame in rats, dogs, and humans to help understand how they administer the safety of such a product.