Reviewing your conversation history is easy!
Open up the "Chat" tab and click on the conversation you want to look back on. You'll see the last few messages of your most recent conversation! Start scrolling up, and you can review the entirety of your previous conversations. You can use the date dividers to keep track of where you are!
If you're on the League.com website on your computer, you can use your browser's search function in order to search through your previous conversations. Scroll up in your conversation to load all of your previous chats, and then push either CTRL-F on Windows or ⌘-F on MacOS to open the 'Find' field. Enter a key word or phrase you're looking for and begin your search!