Discrete and continuous representations of content (e.g., of language or images) have interesting properties to be explored for the understanding of or reasoning with this content by machines. This position paper puts forward our opinion on the role of discrete and continuous representations and their processing in the deep learning field. Current neural network models compute continuous-valued data. Information is compressed into dense, distributed embeddings. By stark contrast, humans use discrete symbols in their communication with language. Such symbols represent a compressed version of the world that derives its meaning from shared contextual information. Additionally, human reasoning involves symbol manipulation at a cognitive level, which facilitates abstract reasoning, the composition of knowledge and understanding, generalization and efficient learning. Motivated by these insights, in this paper we argue that combining discrete and continuous representations and their processing will be essential to build systems that exhibit a general form of intelligence. We suggest and discuss several avenues that could improve current neural networks with the inclusion of discrete elements to combine the advantages of both types of representations.