The visitor/consumer has the option to review the transcript which is delivered via email or saved. The transcript is stored on an archive with a thirteen month rolling window and is available on demand for review. Metadata of the chat activity is stored within CRM.
You can also have 'Transcript Storage' enabled on your account in order for the chat transcript to be duplicated inside your CRM. If you would like this to be enabled on your CRM please let the support team know and they will be able to enable this on your account. The transcripts would then persist past the 13 month window.