Greece is one of the safest countries in Europe and far safer than most areas of the US.
However, no place is perfect.
One of the main "crimes" is pick pocketing or bag snatching, especially in heavily touristed areas of Athens like the Metro and some of the main squares.
However, common sense is your best defense. Keep all personal items close at hand or secure on your person.
I have been to Athens many times, including the Metro and have never had any issues but again no guarantees.
Violent crime is very low and any types of crime are even rate on islands, especially on the more touristy islands.
If you are in Athens you can ask your accommodations if there are any upcoming demonstrations or protests to stay ahead of the game. Even most demonstrations are on the safe side, noisy, crowded but usually safe but should be avoidable.
As usual the media tends to hype up any type of violence so take with a grain of salt.
I would doubt you'd see any type of violence like the Jan. 6 insurrection in Washington, DC
You can check out this informative website for Athens: