Ethan Siegel in Forbes:
If you ask an astrophysicist what's the greatest puzzle in the Universe today, two of the most common answers you'll get are dark matter and dark energy. The stuff that makes up everything we know of here on Earth, atoms, which is in turn made up of other fundamental particles, adds up to only around 5% of the cosmic energy budget. Either 95% of the energy in the Universe is in these two forms, dark matter and dark energy, that have never been directly detected, or something is wrong with our current picture of the Universe. These alternatives have been explored at length, with many options leading to slightly different physical consequences. With the first observation of merging neutron stars, and signals in both gravitational waves and light from across the electromagnetic spectrum arriving, a huge slew of these options have just been ruled out. When put to the test, dark matter and dark energy both survive.
There are a few major puzzles in astrophysics and cosmology that dark matter and dark energy were designed to solve. For dark matter, they largely relate to how galaxies form, rotate, and cluster together; for dark energy, they're about the expansion rate of the Universe and how it evolves over time. If you make an appropriate modification to your theory of gravity, you can alter some of those observables without introducing dark matter and/or dark energy. The hope of those working on these alternatives is that the right modification will be found — one that also makes new predictions distinct from those of dark matter/dark energy — and they can be put to the test.