Incoming links: Grand Unified Theory
As of 2019, the Standard Model and general relativity are incompatible. Once those are unified, we will have one equation to describe the entirety of physics.
There are also however also unsolved problems in electroweak interaction + strong interaction, which if achieved is referred to as a Grand Unified Theory. Reaching a GUT is considered a sensible intermediate step before TOE.
The current state of Physics has been the result of several previous unifications as shown at: en.wikipedia.org/wiki/Theory_of_everything#Conventional_sequence_of_theories so it is expected that this last missing unification is likely to happen one day, potentially conditional on humanity having enough energy to observe new phenomena.
The most important ones are:
- theory of everything. We are certain that our base equations are wrong, but we don't know how to fix them :-)
- full explanation of high-temperature superconductivity. Superconductivity already has a gazillion applications, and doing it in higher temperatures would add a gazillion more, and maybe this theoretical explanation would help us find new high temperature superconducting materials more effectively
- fractional quantum Hall effect 5/2
Other super important ones:
- neutrino mass measurement and explanation