Symbolic knowledge representation and reasoning and deep learning are fundamentally different approaches to artificial intelligence with complementary capabilities. The former are transparent and data-efficient, but they are sensitive to noise and cannot be applied to non-symbolic domains where the data is ambiguous. The latter can learn complex tasks from examples, are robust to noise, but are black boxes; require large amounts of - not necessarily easily obtained - data, and are slow to learn and prone to adversarial examples. Either paradigm excels at certain types of problems where the other paradigm performs poorly. In order to develop stronger AI systems, integrated neuro-symbolic systems that combine artificial neural networks and symbolic reasoning are being sought. In this context, one of the fundamental open problems is how to perform logic-based deductive reasoning over knowledge bases by means of trainable artificial neural networks. In this talk we will present and discuss recent advances made on this topic, and concrete pointers to open research questions.