LEARN ABOUT ARCHIVING MESSAGES ON YAHOO! CHAT
The difference in how Yahoo Messenger for the Web saves archives versus the full Yahoo Messenger program is that on the web messenger, archives are stored on the Yahoo servers and in the full program they are stored directly on your computer.
Here are tutorials about managing your archives:
http://help.yahoo.com/tutorials/ms9/mess/im_archive1.html
Learn about Instant Message History for Yahoo Messenger for the Web: http://help.yahoo.com/l/us/yahoo/messenger/web/web1/history/
And if you ever uninstall/update Yahoo Messenger or get a new computer and want to copy your archives here are the instructions for that: http://help.yahoo.com/l/us/yahoo/messenger/messenger8/messenger/mstacopyarchive.html
Please note that at this time there is no chat history or archiving feature in the Yahoo! Mail chat feature. The most you can do if you want to save a chat session is if you are using the All-New Yahoo! Mail is to turn the chat into an email and send it to yourself. This feature is not available in Yahoo! Classic Mail.
http://help.yahoo.com/l/us/yahoo/mail/yahoomail/chat/chat-08.html;_ylt=AsrVn_4vjpX3HmYC38YUdkhq5yN4