Google just added a new method to their two-step verification security layer implementation, allowing users to merely tap “OK” from within the Google app on their mobile phones to authorize a login:
We know that security is one of your top concerns as a Google Apps admin and that many of you require your employees to turn on 2-Step Verification (2SV) to keep their accounts safe. There are multiple ways your end users can approve sign-in requests via 2SV—by tapping a Security Key, by entering a verification code sent to their phone or, starting today, by approving a prompt like the one below that will pop up on their phone.
Your employees can now choose any of these options in the Sign-in & Security > Signing in to Google > 2-Step Verification section of My Account. The Help Center will be updated with detailed instructions soon; check back here for links to the relevant articles.
The only rather obvious requirement is the phone must have a data connection to receive the notification for approval. This is a smart alternative to SMS-based two-step verification, because the SMS messages themselves can be surveilled, redirected, or stolen, in-transit.