You actually have two questions there because deodorants and antiperspirants are two different things. By itself, sweat doesnt have a lot of odor. But the bacteria that live in our armpits and eat skin cells, oil, and such produce smelly byproducts.

Antiperspirants plug up our sweat glands so that we sweat less. A drier environment also discourages bacteria. People who are afraid that others will see them sweat through their clothes in stressful situations may use antiperspirants.

Deodorants dont keep us from sweating, but they keep bacteria populations down by poisoning them with acids, salts, or other things. These substances are usually too mild to bother us humans, but some people are sensitive to them. Our skin is covered with bacteria, so once the deodorant wears off, new bacteria move in. By the way, lots of the bacteria in and on our bodies help us, so try not to be grossed out by thinking about them.

Many products also have strong odors of their own that can cover up some of the sweat odor, but some people find these odors worse than the body odor. Some products contain deodorants and antiperspirants, plus camouflaging perfumes.

Sweat actually serves useful functions. It cools us off when we get too hot. It allows us to get rid of some wastes, and it may even be a way to communicate.

Lots of people are interested in the study of sweat. Lie detectors or polygraph tests record sweating (among other things). I found some stories that propose using sweat to detect drug use or tell who is really stressed out to identify dangerous people. Some studies have shown that mosquitoes can use the odor of sweat to find their next victims.

If you wanted to test which product was best at stopping body odor, how could you do it? It might be a good science fair project.

Deodorants are different from antiperspirants. A deodorant applied to the body eliminates body odor caused by the bacterial breakdown of perspiration. The antiperspirants are made of aluminum chlorohydrate and aluminum-zirconium compounds.These aluminum-based complexes react with the electrolytes in the sweat and form a gel plug in the duct of the sweat gland. It is this plug which prevents the gland from excreting liquid.

I recommend you to go to the next link and read more about deodorants and antiperspirants, their compounds, toxicity, etc.

Most deodorants that you buy in the store today are paired with antiperspirant. The active ingredient in these antiperspirants is an aluminum compound. As cells absorb this compound they also absorb water, causing them to swell. As swelling increases, the cells eventually seal the duct from your sweat gland, which prevents the sweat from reaching the surface. However, this process only works for so long, and eventually the cells release the water through osmosis in order to reach equilibrium with the environment outside of the cell. This is why you have to keep applying the deodorant/antiperspirant throughout the day. I have included a link that goes into more detail about how this works, such as specific compounds that are often used. Also, I would like to add that it is the acidity of these antiperspirants and not the sweat itself that actually causes the stains that often form on shirts.