Over the last decade, deep learning has shown great success at performing computer vision tasks, including classification, super-resolution, and style transfer. Now, we apply it to data compression to help build the next generation of multimedia codecs. This thesis provides three primary contributions to this new field of learned compression. First, we present an efficient low-complexity entropy model that dynamically adapts the encoding distribution to a specific input by compressing and transmitting the encoding distribution itself as side information. Secondly, we propose a novel lightweight low-complexity point cloud codec that is highly specialized for classification, attaining significant reductions in bitrate compared to non-specialized codecs. Lastly, we explore how motion within the input domain between consecutive video frames is manifested in the corresponding convolutionally-derived latent space.