If the headphone receives digital input, one can apply all kind of DSP before the DA conversion.
A very popular one is ANC (Active Noise Cancellation).
The noise of the environment is captured by a microphone.
Use a complex algorithm, the inverse of this noise is added to the music.
When done right the outside noise and the inverted noise in the music should cancel out each other. Practice might be a bit different.
Sennheiser Momentum Wireless headphone with noise cancellation
EQ has become very popular.
Some go even as far as that you can make any headphone sound like any other by applying the proper EQ.
I do think this a bit too optimitic but EQ can compensate for a lot af anomalities in the freqency response.
More about EQ.
Sennheiser MOMENTUM True Wireless comes with an app.
You can mix the audio and the environment.
You can also equalize.
This setting is stored in the headphone hence active all the time.
Up to today I haven't found out how to lower the bass without altering the rest.
Horrible interface.
A rare combination of over the ear plus in-ear
It claims to compensate by measuring the response
"The nuraphone plays a range of tones into the ear, and then measures a very faint sound that your ear generates in response to these tones called the Otoacoustic Emission (OAE). This tiny signal originates in the cochlea and vibrates the ear drum, turning it into a speaker and playing sound back out of your ear. Yes our ears make sound! This sound is about 10,000 times smaller than the sound that went in.
Encoded in the returning sound wave is information about how well you heard the sound that went in. The nuraphone uses an extremely sensitive microphone to detect this returning sound wave, and a self learning engine built into the nuraphone to create your profile. No buttons or knobs. It all happens automatically and in about 60 seconds. It is a little bit magic.
Once the nuraphone has created your hearing profile it sonically moulds your music so that it matches your hearing system and delivers all the detail of the music you love. Once personalised you can listen to your favorite music in stunning detail from your favorite player."
Source: Nuraphone
A portable Bluetooth receiver
Measure your ears with Aumeo Headphone Personalizer's companion app, AumeoHub (iOS & Android). 8 frequency bands will be measured for each ear.
This is a Graphic equalizer.
Using an app, you to calibrate the headphones to your specific hearing profile.
ANC (Active Noise Cancellation)
Bluetooth 4.2
Hands free calling
Over the ear Bluetooth headphone.
Cleverly marketed as “glasses for your ears” the user supplies his equal loudness contour using an app.