You'll find a variety of answers in the FAQ about this question, though for such a broad topic I'm sure there is much more to be said.

(FAQ answers are from /u/mimicofmodes, /u/sunagainstgold, /u/cthulhushrugged, /u/churakaagii, /u/mimicofmodes, /u/AnotherPersonAH, and /u/Tiako.)

Romans typically wore their hair short without beards for practical militaristic reasons - hygiene and so your enemy couldn’t grab loose hair. This style was popularised by Scipio Africanus , who is regarded as one of the greatest Romans of all time , who wore his hair short and kept himself clean shaven