Graph autoencoders (GAE) and variational graph autoencoders (VGAE) emerged as two powerful groups of unsupervised node embedding methods, with various applications to graph-based machine learning problems such as link prediction and community detection. Nonetheless, at the beginning of this Ph.D. project, GAE and VGAE models were also suffering from key limitations, preventing them from being adopted in the industry. In this thesis, we present several contributions to improve these models, with the general aim of facilitating their use to address industrial-level problems involving graph representations. Firstly, we propose two strategies to overcome the scalability issues of previous GAE and VGAE models, permitting to effectively train these models on large graphs with millions of nodes and edges. These strategies leverage graph degeneracy and stochastic subgraph decoding techniques, respectively. Besides, we introduce Gravity-Inspired GAE and VGAE, providing the first extensions of these models for directed graphs, that are ubiquitous in industrial applications. We also consider extensions of GAE and VGAE models for dynamic graphs. Furthermore, we argue that GAE and VGAE models are often unnecessarily complex, and we propose to simplify them by leveraging linear encoders. Lastly, we introduce Modularity-Aware GAE and VGAE to improve community detection on graphs, while jointly preserving good performances on link prediction. In the last part of this thesis, we evaluate our methods on several graphs extracted from the music streaming service Deezer. We put the emphasis on graph-based music recommendation problems. In particular, we show that our methods can improve the detection of communities of similar musical items to recommend to users, that they can effectively rank similar artists in a cold start setting, and that they permit modeling the music genre perception across cultures.