Breathing Compensation is a very creative and useful feature that was implemented first on the Sony Alpha A7 IV full-frame mirrorless camera. Today Sony's full-frame Cine camera Sony Sony FX6 became the second camera to have this feature by a firmware update V2.0 which proves that this can be added to more existing cameras such as Sony Alpha A1 and Sony Alpha A7S III in the future via a firmware update.
Update December 7, 2022: Recently announced Sony Alpha A7R V also has the Lens Breathing Correction feature.
Update December 23, 2022: Canon released their version of Lens Breathing Compensation
Sony A7 IV First camera to feature Focus Breathing Compensation
Breathing Compensation function adjusts the size of the frame dynamically in-camera during video recording by applying a certain percentage of crop in order to minimize the phenomenon called Lens Breathing, where the angle of view changes according to the focusing distance. Specially designed cine lenses are corrected for lens breathing but they are generally quite expensive, large and lacking autofocus so they are mostly out of reach and impractical for many users. But thanks to Sony engineers, this effect is now corrected with a software implementation without the need of special cine lenses.
The current limitations with Sony's implementation is that it only works with the compatible certain Sony E-Mount lenses that are listed below. We don't know if Sony will expand the compatibility to its other E-mount lenses, and even better give the 3rd party manufacturers the access to this feature (we hope they do) but for now, Sony A7 IV shooters (and the FX-6 shooters) are limited with the lenses below.
List of Breathing Compensation Compatible Sony Lenses
Sony FE 14mm F1.8 GM - Amazon, BH Photo
Sony 20mm F1.8G - Amazon, BH Photo
Sony FE 24mm F1.4 GM - Amazon, BH Photo
Sony FE 35mm F1.4 GM - Amazon, BH Photo
Sony FE 50mm F1.2 GM - Amazon, BH Photo
Sony FE 50mm F1.4 GM - Amazon, BH Photo
Sony FE 85mm F1.4 GM - Amazon, BH Photo
Sony FE 100mm F2.8 STF GM OSS - Amazon, BH Photo
Sony FE 135mm F1.8 GM - Amazon, BH Photo
Sony 12-24mm F2.8 GM - Amazon, BH Photo
Sony FE 12-24mm F4 G - Amazon, BH Photo
Sony FE 16-35mm F2.8 GM - Amazon, BH Photo
Sony FE PZ 16-35mm F4 G - Amazon, BH Photo
Sony FE 20-70mm F4 G - Amazon, BH Photo
Sony FE 24-70mm F2.8 GM - Amazon, BH Photo
Sony FE 24-70mm F2.8 GM II - Amazon, BH Photo
Sony FE 24-105mm F4 G OSS - Amazon, BH Photo
Sony FE PZ 28-135mm F4 G OSS - Amazon, BH Photo
Sony FE 70-200mm F2.8 GM OSS - Amazon, BH Photo
Sony FE 70-200mm F2.8 GM OSS II - Amazon, BH Photo
There are 20 lenses that are compatible with the Breathing Compensation feature so far as seen on this list. 14 of these lenses are GM (G Master) lenses and the remaining for are the G-Lenses so no real budget lenses are on this list, we hope Sony increases the number of compatible lenses in the future.