Don't worry, your ability to delete emails hasn't gone away
With the latest update to the new Gmail interface, Google has moved things around a bit -- unfortunately, it didn't give users much indication of how things changed. One of the big headaches that re-surfaced after the latest update was Google's differentiation between archiving and deleting emails, and what options are chosen to be available. We went through this with the last couple large updates to Gmail that introduced swipe-to-delete and actionable notifications, and we wanted to provide a quick refresher on how to manage your archive and delete options in the new Gmail interface.
If you haven't tweaked any settings previously, you'll be hard-pressed to find a delete option from any view of the Gmail app -- this unfortunately doesn't change in the latest update. Fortunately, this can be changed quickly and easily from the app settings, found by tapping "Menu", "Settings" and then "General settings". The top setting, appropriately labeled "Archive & delete actions" controls which options will become available in the top action bar when you select emails from your inbox or a message view. You'll have three options -- archive only, delete only and archive & delete -- which are pretty self explanatory.
This setting acts as a global control anywhere that the app would need user input to either archive or delete messages. For example when you multi-select messages from a list view, you will see either an archive icon, delete icon or both available in the top action bar. The same is true when you enter an individual email, when you swipe away an email from the inbox view, or when you expand an email notification on Jelly Bean devices. Your setting selection is applied to every part of the app -- so choose wisely here based on your own email retention habits.
Below we have a video breakdown of the whole process of changing archive and delete functions in the settings of the new Gmail interface.