Dark matter is not a theory, per se. There are many, many theories that attempt to explain dark matter. Some of them have yet to produce testable hypotheses, others have already been tested.
The issue that I have with people calling dark matter a theory is that they think it requires matter to solve. It doesn't. MOND is a dark matter theory. It explains(in part) why it appears as though undetectable matter is present in galaxies causing disc velocity to not match expectations.