There are 8 officially recognized disciplines in freediving:
Constant Weight (CWT)
The freediver uses a monofin or bi-fins and the body’s own power to propel down and up again.
Here Guillaume Nery (France) dives to 109 m:
Constant Weight No Fins (CNF)
The freediver uses only arms and legs to perform the dive, swimming breaststroke down and back up.
See world record holder William Trubridge freediving the Arch in Dahab, Egypt:
Free Immersion (FIM)
The freediver dives under water without the use of propulsion equipment, but only by pulling on the rope during descent and ascent.
Andreas Güldner dives to 72 m (FIM):
Static apnea (STA)
The freediver holds his breath for as long as possible while laying face down in the water.
Eric van Riet Paap holds his breath for 7:33 in competition:
Dynamic with fins (DYN)
Using bi-fins or a monofin the diver swims horizontally as far as possible under water.
Here Peter Pedersen swims 200 m under water.
Dynamic No Fins (DNF)
Swimming breaststroke underwater the diver goes as far as possible.
On this video you can see Dave Mullins from New Zealand setting the current world record:
No Limits (NLT)
Going down with a sled, and going back up with a balloon, a diving suit or a vest with inflatable compartments, or whatever other means.
Herbert Nitsch’s No limits dive to 214 m:
Variable Weight (VWT)
The athlete utilizes ballast (sled) for the descent but has to get back to the surface using only his own power, either swimming, finning, or pulling on the rope.
Carlos Coste diving to 141 m:
You can check out the World Records in these disciplines in the Records section.