It may shocking to learn that all the particles that we know of, everything that is made out of atoms and molecules, and therefore everything you see when you look out into the sky, only accounts for about 5-6% of the total energy budget of the universe. The rest of the universe is unknown to us. 25% of the universe is dark matter and likely made of particles yet to be identified. About 70% is dark energy, which is something even more exotic, not made out of particles.
We know of the existence of dark matter because all that invisible mass makes itself known through its gravitational pull. Its presence is even imprinted in the earliest snapshot of the universe we have access to, the cosmic microwave background.
Now, according to the rules of particle physics, it is entirely possible for two types of particles to only interact through gravity. It is possible therefore for a dark matter particle to pass through solid matter, as if it were a ghost. If that were the case, we may simply not have any chance of ever discovering individual particles of dark matter.
However, some of the plausible hypotheses that have been proposed to answer open questions in particle physics, combined with the specific amount of dark matter that we know is out there, suggest to us that there may exist a very low chance that dark matter would interact with a visible particle. As a result, a dark matter particle would still behave mostly like a ghost, but now there would be a limit (albeit an astronomical one) to how much solid matter it could pass through until it eventually collides with an atom.
If this is true, it gives us multiple ways to look for dark matter particles in experiments. For dark matter particles whose mass and interaction probability lie in a specific range suggested by the theories mentioned above, three types of experiment become particularly exciting. The first is to look for energetic visible particles created when dark matter particles and their antiparticles destroy one another in the universe. This is referred to as indirect detection. The second is to set up experiments where we carefully monitor atoms to see whether any of them experience a collision with one of the myriad dark matter particles passing through the experiment. This is referred to as direct detection. The third is to artificially create dark matter particles by colliding visible particles in particle accelerators. Each of these three possibilities is being explored by a number of ongoing experiments.