The existence of worms holes has been long debated and has even become a staple in science fiction
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They may exist between every particle, because of quantum entanglement
Worm holes, aka Einstein Rosen bridges, may be present as a connection between every entangled particle, but when collected in large amounts may be traveled into. However, this is only for black holes which are made out of particles entangled with those of another.
Quantum entanglement is common in quantum mechanics. It happens when two groups of particles are correlated in some way. Perhaps they were created together or simply bumped into each other. At maximum entanglement you can measure any property of one particle and know that of the other. When one is measured the other will have the opposite properties. Each particle has the properties of spin, position, momentum and polarization. For example, if a particle has the spin of -1 the one it is entangled to will have a spin of +1. If you drew a line through where they interacted you would see their positions are mirror opposite of each other and so on. Entanglement doesn't have to be maximum a particle can be entangled with only a few of its properties. You can measure any property of one but not every. When you measure something that small you change it, this means that you can not measure every possibility. Because you have to shoot a few electrons or photons in its general area. However, a particle doesn't seem to pick a position until it has been measured. Which means it must "communicate" in some way.
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Entanglement of space
Space can be entangled and may actually be a product of it. (in video below or here.) This has implications concerning black holes.
However entangled black holes create a paradox.
(This is covered in Stanford lecture video below)
Things may only be maximally entangled to one other thing (because if it has been entangled with something else it has been changed and is not maximal). In general relativity black holes have a smooth horizon where nothing fancy happens. When a black hole is maximally entangled, everything that happens inside the black hole must be correlated with what is inside the other black hole. The horizon of a black hole must have entangled space on either side of the horizon. The space can not be entangled with the other black hole and stuff on the outside edge of the black hole's horizon.
Many solutions to the paradox have been thought up. Most do not make the cut, for example, the inside of a black hole simply not existing. That would go against general relativity or the firewall theory which violates it and would mean the loss of information (which is an even bigger no-no). Since things can not be entangled to multiple things hawking radiation, which has to be entangled with the black hole and other hawking radiation to stop information loss, once the particles the radiation is entangled to enters the black hole it stops being entangled. This would release a huge amount of energy. Which would mean the horizon of the black hole is not smooth but burns everything that comes into it.
(hawking radiation is radiation that comes from a black hole. A particle and antimatter particle, for example, are created just outside the event horizon. One falls in the other escapes never to combine with the other one.
A solution to the paradox was needed, one where quantum entanglement was not violated
If a space is shared between black holes, interacting with the particle on the outside would be able to
actually effect the one inside the other black hole. However, the one inside the black hole can never effect the other one as the signal will never reach it.
This is the ER=EPR theory. ER stands for Einstein Rosen (which was a paper written by both of them on what we call wormholes aka Einstein Rosen bridges). EPR stands for Einstein Podolsky Rosen (another paper written on quantum entanglement). The theory goes that they are actually the same thing as talked about above.
Properties of the Einstein Rosen bridge
The Einstein Rosen bridge is a piece of space connecting the black holes. Since it is inside black holes it is impossible to leave. That means no signal can pass all the way through. However, it is possible to meet in the middle. This you can receive information from any distance away. Although it does have the drawback of death and the ability to only do it once. Have fun.
The size and shape
You can imagine the space inside of a black hole expanding faster than the speed of light. You can image it as a 3d bridge that has each black hole on each end. The bridge has a finite size in two dimensions while the 3rd (in the directions of the black holes) is expanding. The two dimensions or the "cross sectional area" is a product of all of the Einstein Rosen bridges between the particles in the singularity.
One particle would mean it is likely one Planck-width squared. Which is so small it would take about 10^72 entangled particles to be able to fit our body through. Which would be an impressive find.
They are untestable (well unless you want to prove it for yourself only and die) and only one of the more common solutions to a paradox.
(A Stanford lecture by Leonard Susskind a physics professor )
@justtryme90 helped a lot with this. If you haven't already go follow him.