My first impression, just looking through pictures of sailing ships, is that there were perhaps little, eh, "latrines" inside larger ships during the Exploration Age where a crewman could relieve himself. But looking at images of biremes and triremes, I get the feeling that Greek and Roman seafarers simply went over the side.
Are there any flaired users with knowledge of this mundane aspect of early seafaring life?
This gets asked here from time to time. Check out this older answer that u/davidAOP and I collaborated on.