Glues and other adhesives have been around for at least 6000 years. Thousands of years ago people repaired broken pottery with sticky resins from tree sap. Adhesives were made from egg whites. Beeswax and tar were used to caulk the spaces between the planks of ships.
In the 1750s the British issued a patent to make a fish glue. By 1900 many factories in the U.S. produced glue.
Today, there are super-strong adhesives that hold protective tiles on the Space Shuttle, and adhesives (like Velcro) that work without the use of chemicals. Medical professionals have a special glue that bonds skin together, avoiding stitches.
So how adhesives work depends on the type of adhesive.
White glue, commonly used in the classroom of elementary school students, works through evaporation. The water in the white glue evaporates and the polyvinyl-acetate latex (a non-toxic substance) that remains forms a flexible bond. Because white glue dries by evaporating, white glue dries faster on wood (because wood absorbs some of the water) than leather (which doesn't absorb water, so the water in the glue must evaporate completely). Although white glue (such as Elmer's Glue) generally dries in 20 to 30 minutes, it takes 24-hours for the bond to reach its full strength.
Have you heard about the "glue factory"? Some adhesives do use animal hides and bones as ingredients, but many glues use chemicals unrelated to animals.
A very simple glue can be made by mixing flour and water (it won't be very strong, but it will hold two pieces of paper together).
The main ingredient in Super Glue (and Krazy Glue) is cyanoacrylate (an acrylic resin). The cyanoacrylate molecules begin lining up into chains when they come into contact with water, and when the cyanoacrylate molecules can no longer move, the glue is hard. Because nearly everything has at least a trace amount of water on it (if only from the moisture in the air), Super Glue works on just about anything.
Avoid getting Super Glue on your skin (since there is water there). Elmer's also makes a Krazy Glue Skin Guard, which bonds to almost everything except skin.
As you can see, there are different glues that meet many different needs.
A woodworker might use Gorilla Glue, which is a polyurethane glue that becomes sticky because of a reaction between the polyurethane, oxygen, and water (water is the catalyst). But even though water is needed for the reaction, once cured Gorilla Glue is waterproof and can even be used on the underwater parts of boats.
Duct tape and Scotch tape are also adhesives.
So is Velcro.
Velcro was developed after a Swiss inventor took a walk with his dog in the 1940s and noticed that his pants were covered with burrs. The inventor looked at the burrs under a microscope and noticed a hook shape to them. He then came up with a system of two tapes: one with J-shaped hooks, and the other with a fuzzy nap. The materials weren't "sticky" in the regular sense, but they stuck to each other.
Currently, a scientists are trying to invent a tape based on the sticky feet of geckos.
Like Velcro, a gecko's tiny foot has a hundred thousand microscopic hairs called setae, rather than chemicals. The tips of the setae separate into 1,000 tips so small that it takes an electron microscope to see them. These tips use what's called the van der Waals force between molecules. Dutch physicist Johann van der Waals won the Nobel Prize in physics in 1910. He discovered the weak attractive force between atoms or molecules that result from the positioning of the electrons within the interacting particles. Although the forces are very weak, they're strong enough that when you slow down the molecules of a gas by cooling it, the molecules stick together enough to become a liquid. The same process is at work when a liquid becomes a solid.