Where can I see the emails I send as replies to the submissions?

I can't see the email correspondence and can't figure out where to access it.

Are you referring to the emails you sent by replying to the submissions data within your form submissions page? If yes, there's no way to check them in your form submissions page. Only submissions data you received from your form are stored in your form submissions page. 

However, you can review the emails you've sent by checking them in your email history.

http://www.jotform.com/help/293-How-to-view-all-your-form-Email-History

Thanks!