Open email at 2 different computers: 1 @ work/ 1 @ home

I have several email accounts. I check them at home and at work. If I have looked at home, say, (I guess you would say it was downloaded)…then when I open that same email account at work, the ones I saw at home do not show up again. How can I manage this so that I can see them at both places. Is this possible. I have been keep them on the “server” of the isp…but this cumbersome and I still cannot reply properly and keep it in my contact sequence. Does anyone understand this problem…what to do?