Image compression standards rely on predictive coding, transform coding, quantization and entropy coding, in order to achieve high compression performance. Very recently, deep generative models have been used to optimize or replace some of these operations, with very promising results. However, so far no systematic and independent study of the coding performance of these algorithms has been carried out. In this paper, for the first time, we conduct a subjective evaluation of two recent deeplearning-based image compression algorithms, comparing them to JPEG 2000 and to the recent BPG image codec based on HEVC Intra. We found that compression approaches based on deep auto-encoders can achieve coding performance higher than JPEG 2000, and sometimes as good as BPG. We also show experimentally that the PSNR metric is to be avoided when evaluating the visual quality of deep-learning-based methods, as their artifacts have different characteristics from those of DCT or wavelet-based codecs. In particular, images compressed at low bitrate appear more natural than JPEG 2000 coded pictures, according to a no-reference naturalness measure. Our study indicates that deep generative models are likely to bring huge innovation into the video coding arena in the coming years.