Almost no phone has a headphone socket any more. This is what lets a wired pair, or a wireless pair in cable mode, play from your phone when the battery dies.
What to look for: Look for one that states a built-in DAC and a sample rate. Passive adapters only work with phones that still output analogue.
Many seat-back screens still use two 3.5 mm prongs. Without this, the headphones you bought for flying cannot play the film. Check your pair has a 3.5 mm socket first.
What to look for: Gold-plated contacts and a short body, so it does not hang out of the armrest.
Worn pads leak, and a leaking seal costs more noise cancelling than any firmware update can win back. It is the cheapest upgrade there is for a pair you already own.
What to look for: Pads are model-specific: XM6 and XM5 pads do not swap. This set is for the XM6.
For sleeping, mowing or a loud concert, foam beats every pair on this site and costs a few dollars. We would rather say so than sell you headphones for the job.
What to look for: A noise reduction rating printed on the box, and a size that does not ache after an hour.