Yahoo Messenger for Windows, Mac, iOS and Web platforms comes with a lengthy feature list, encompassing everything from photo sharing to call forwarding to customized user avatars. As its name implies, the meat of this long-running program lies in its instant messaging features; as an IM app, Messenger has the basics covered, including the ability to access a conversation history log.
Access "Contacts" from Yahoo Messenger's menu, then select "Conversation History." This provides a list of conversations you've had, displayed in chronological order.
Choose "Participant" if you'd rather arrange the conversations alphabetically by the name of the Yahoo user with whom you conversed.
Select the conversation of your choice -- indicated by the username of the person with whom you chatted and the first line of the conversation -- to view a transcript of the exchange.