Current unexplained phenomena in physics include
The phenomena which do not fit pose severe problems for the existing theories, in part because of the extreme accuracy of their predictive power elsewhere.
In order to try to explain these phenomena, scientists are searching for new deeper theories which will explain all observed phenomena, as well as exploring ways to amend their current theories. Highly mathematical work on finding new deeper theories includes the programs of M-theory and loop quantum gravity. More "physical" ad-hoc theories to amend current theories include modified Newtonian dynamics and doubly-special relativity.