We review a class of methods that can be collected under the name nonlinear transform coding (NTC), which over the past few years have become competitive with the best linear transform codecs for images, and have superseded them in terms of rate--distortion performance under established perceptual quality metrics such as MS-SSIM. We assess the empirical rate--distortion performance of NTC with the help of simple example sources, for which the optimal performance of a vector quantizer is easier to estimate than wit…