Facebook will also let you back in via a "Trusted Friends" feature, no text messaging required.
Trusted friends are friends you can reach out to if you ever get locked out of your Facebook account (ex: you turn on login approvals and then lose your phone, you forget your Facebook password and can’t get into your login email account to receive a password reset). If you get locked out, we’ll send each of your trusted friends a security code. All you need to do is call your friends and collect the codes.
You’ll only need 3 codes to get back into your account, but we recommend picking 5 trusted friends so you have back-up. Your trusted friends should be people you can easily call and who are likely to respond to you quickly.
You can pick your trusted friends from your Security Settings page.