Diagrams have been shown to be effective tools for humans to represent and reason about complex concepts. They have been widely used to represent concepts in science teaching, to communicate workflow in industries and to measure human fluid intelligence. Mechanised reasoning systems typically encode diagrams into symbolic representations that can be easily processed with rule-based expert systems. This relies on human experts to define the framework of diagram-to-symbol mapping and the set of rules to reason with the symbols. This means the reasoning systems cannot be easily adapted to other diagrams without a new set of human-defined representation mapping and reasoning rules. Moreover such systems are not able to cope with diagram inputs as raw and possibly noisy images. The need for human input and the lack of robustness to noise significantly limit the applications of mechanised diagrammatic reasoning systems. A key research question then arises: can we develop human-like reasoning systems that learn to reason robustly without predefined reasoning rules? To answer this question, I propose Neural Diagrammatic Reasoning, a new family of diagrammatic reasoning systems which does not have the drawbacks of mechanised reasoning systems. The new systems are based on deep neural networks, a recently popular machine learning method that achieved human-level performance on a range of perception tasks such as object detection, speech recognition and natural language processing. The proposed systems are able to learn both diagram to symbol mapping and implicit reasoning rules only from data, with no prior human input about symbols and rules in the reasoning tasks. Specifically I developed EulerNet, a novel neural network model that solves Euler diagram syllogism tasks with 99.5% accuracy. Experiments show that EulerNet learns useful representations of the diagrams and tasks, and is robust to noise and deformation in the input data. I also developed MXGNet, a novel multiplex graph neural architecture that solves Raven Progressive Matrices (RPM) tasks. MXGNet achieves state-of-the-art accuracies on two popular RPM datasets. In addition, I developed Discrete-AIR, an unsupervised learning architecture that learns semi-symbolic representations of diagrams without any labels. Lastly I designed a novel inductive bias module that can be readily used in today’s deep neural networks to improve their generalisation capability on relational reasoning tasks.