There are several different fitting systems for PEX tubing; most being proprietary, that create a water tight seal between the fitting and the PEX without the use of chemicals or heat. The most common joining methods are shown below:
PEX ring expansion method (ProPEX)
This type of joining system is very robust and creates a reliable joint but requires an expansion tool with a different head for each size of tubing. This type of joint is made by placing a PEX ring over the end of the tubing and expanding the tubing until a fitting can be pushed in and the "memory" of the PEX shrinks onto the fitting. It is recommended that joints made with the ProPEX system be allowed to stand for 24 hours before pressurized.
Formerly known as Wirsbo the company is now owned by Uponor and is the supplier of this systems tools and materials.
Metal sleeve expansion system (EVERLOC)
REHAU is the sole provider of this system (as far as I know) and has proven very reliable; although more expensive, than other PEX systems. EVERLOC joining is used for potable water distribution system but is most commonly used for radiant heating and cooling applications. Joints are made by expanding the end of the tubing and inserting a barbed fitting, then a metal sleeve is pulled down over the tubing using a tool to create a tight seal. One benefit of this method is that once the metal sleeve is in place the joint can be pressurized.
Crimp ring PEX connections
This is one of the most used joining methods for PEX as it is non proprietary and readily available at most hardware stores. Unlike the first two methods discussed this method does not expand the tubing over the fitting but instead uses a smaller inside diameter fitting that can be pushed inside the tubing and is "crimped" onto the fitting. The rings are usually made of copper and will require a tool that has the proper size orifice to crimp it. Fittings may be made of copper, brass, bronze or plastic and will have barbed ribs.
Cinch ring method for joining PEX
This probable the simplest joining method for making PEX connections. A single tool can cinch rings up to 1" in diameter and will only release once a properly cinched joint is made. Both the rings and the cinch tool are fairly cheap and can be found at most hardware stores.
Push type PEX connections
These are my least favorite type of PEX fittings, as they are over priced and leave room for error. Push type fittings are made by a few different companies but operate on the same principle, the tubing is pushed into the fitting and is held in place by a stainless steel grip ring. These fittings do not require any specialized tools, just a square cut on the end of the tubing. These fittings may not be allowed by your local plumbing code