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The increasing digitization and datification of all aspects of people's daily life, and the consequent growth in the use of personal data, are increasingly challenging the current development and adoption of Machine Learning (ML). First, the sheer complexity and amount of data available in these applications strongly demands for ML algorithms that can be trained directly on complex structures, which can be naturally described by graphs. In fact, graphs inherently capture information about entities, their attributes, and relationships between them. Directly applying ML to graphs relieves domain experts and data scientists from the challenging and time-consuming problem of designing a suitable vector-based data representation used by classical ML techniques. Second, ML algorithms should not only be designed to achieve high technical and functional standards; as the automated decisions provided by these algorithms can have a relevant impact on people's lives, their behavior has to be aligned with the values and principles of individuals and society. This demands for designing automated algorithms that we, as humans, can trust, fulfilling the requirements of fairness, robustness, privacy, and explainability. Third, designing effective ML algorithms requires skills and expertise developed at different levels. This substantially hinders the democratization and widespread availability of such technology for society at large, which in turn demands for improving the level of automatization and systematization of their design process, while also providing guarantees on their performance. For this reason, this paper provides an overview of the current works focused towards learning trustworthily, automatically, and with guarantees on graphs. [ABSTRACT FROM AUTHOR]