Anamorphic lenses allow a widescreen picture to fit in a normal frame without letterboxing. This is accomplished by optically squeezing the image horizontally. While technically unnecessary today, filmmakers continue to use anamorphic lenses for their cinematic aesthetic.
Anamorphic images stay squeezed throughout the entire visual effects pipeline. For convenience they are displayed as unsqueezed in most software packages, but this is only superficial.
The squeezing is defined by the image’s pixel aspect ratio. The standard pixel aspect ratio is 1.0 (square). The most common anamorphic pixel aspect ratio is 2.0. For anamorphic shots the virtual camera’s film back width is multiplied by the pixel aspect ratio. This is usually around double, as in the case of CinemaScope (2.0).

CinemaScope 35 mm film (2K scan):
Squeezed (actual) = 1828 x 1556
Unsqueezed (display) = 3656 x 1556
Physical film back = 21.936 mm x 18.672 mm
Virtual film back = 43.872 mm x 18.672 mm

Anamorphic Flowchart:

1. original plate
2. remove lens distortion (undistort plate)*
3. camera tracking/matchmove
4. cg pipeline (undistorted)
5. render cg with overscan (undistorted)**
6. distort cg render
7. composite over original plate

* Step 2 assumes a lens distortion grid was photographed or lens mapping data was acquired. Step 2 is often part of step 3. Camera tracking software can calculate lens distortion from most plates.

** Step 5 is required when undistorting barrel distortion. If overscan is not rendered the edges of the frame will be cropped when distortion is applied.

Wikipedia: Anamorphosis
Wikipedia: Anamorphic Format
Wikipedia: Pixel Aspect Ratio
RED – Learn: Understanding Anamorphic Lenses
ARRI ALEXA Anamorphic De-squeeze White Paper
SynthEyes Lens Distortion and Anamorphic Padding White Paper
3DEqualizer4 R3 [exercise] Anamorphic Distortion and Lens Breathing
http://www.metrics.co.uk/support/solution_view.php?id=1563
http://www.metrics.co.uk/support/solution_view.php?id=1528
https://www.ssontech.com/content/lensflo.html