Thanks a lot for passing by and this very interesting question.
First of all, one should note that current experiments do not have the capacity to explore all possibilities for dark matter. Therefore, not finding anything does not necessarily mean that dark matter is not there. This would only mean that if we have dark matter, it will be harder for us to find it (as we may need to design new strategies for instance).
For that reason, while current experiments are running, the next generation of experiments are being designed and built, with an increased sensitivity and possibly ways to probe configurations to which we are not sensitive yet. For now, prospects are great for the next couple of decades (at least). We still have ideas and there is still room for dark matter to be there.
I guess your question is about what will happen if dark matter is eventually not there? Well, I don' know. Maybe MOND would be the right theory after all (i.e. a theory in which the way gravity works is modified), or maybe dark matter will just be more exotic than naively thought (I doubt that we will be able to probe all options within the next 50 years, at least). To conclude, what is important is that we have options to explore, as this means we will have ideas about how to probe the full thing further and maybe revolutionise our understanding of cosmology (the currently best model includes dark matter).
I know I didn't answer properly the question, but I guess there is no good answer too ;)
Thank you very much! Yes, my question was aimed at just that, whether there was any other theory that could give an explanation dispensing with dark matter, in case in the long run all attempts to find it failed. I read a bit about MOND theories and, although my knowledge of physics is not enough to understand them more than superficially, they don't seem to have much acceptance in the scientific community. So, as you say in your answer, the best way forward, at least for a few decades, is to keep looking for dark matter.
There are a bunch of physicists who work on modified gravity theories (that include MOND). The reason why most of us focus on dark matter is because in terms of significance this idea is stronger. This however does not mean that modified gravity theories are excluded and that no one cares about them. They are tested too.
At the end of the day, what is important is that all paths are explored, which is the case.
Thanks for the answers! Dark matter seems like a very exciting field to be working in at the moment.
I fully agree. :)
This is why I have dedicated a significant fraction of my research time to dark matter during the last 5-6 years.