Closely cropped hair was a necessity of soldiers and short hair became a standard for men during the middle and late Republic, and into the early Empire. men would also also be clean shaven, even though the process of shaving without todays modern advancements was uncomfortable and frequently resulted in cuts and scratches.
It was the emperors who's celebrity status would bring about the most change. The emperor Nero created an elaborate hairstyle with curls framing his face that became very popular. Later he would add short sideburns, which can also be seen on his coins. The emperor Hadrian was the first emperor to adopt a short beard, and many men would follow his example, no doubt happy to avoid the ordeal of shaving. Even after Hadrian's reign ended beards would become quite common among Roman men.
Womens hairstyles, along with jewelry, defined their socal standing. Aristocratic women wore elaborate styles and would often mimic the empress of the time. One of the most famous styles was that of the Flavian era, in which women would keep high curls on on the front of their head and a tight bun in the back.