Abstract: Neural data compression based on nonlinear transform coding has made great progress over the last few years, mainly due to improvements in prior models, quantization methods and nonlinear transforms. A general trend in many recent works pushing the limit of rate-distortion performance is to use ever more expensive prior models that can lead to prohibitively slow decoding. Instead, we focus on more expressive transforms that result in a better rate-distortion-computation trade-off. Specifically, we show that nonlinear transforms built on Swin-transformers can achieve better compression efficiency than transforms built on convolutional neural networks (ConvNets), while requiring fewer parameters and shorter decoding time. Paired with a compute-efficient Channel-wise Auto-Regressive Model prior, our SwinT-ChARM model outperforms VTM-12.1 by $3.68\%$ in BD-rate on Kodak with comparable decoding speed. In P-frame video compression setting, we are able to outperform the popular ConvNet-based scale-space-flow model by $12.35\%$ in BD-rate on UVG. We provide model scaling studies to verify the computational efficiency of the proposed solutions and conduct several analyses to reveal the source of coding gain of transformers over ConvNets, including better spatial decorrelation, flexible effective receptive field, and more localized response of latent pixels during progressive decoding.