Abstract: Machine reasoning research aims to build interpretable AI systems that can solve problems or draw conclusions from what they are told (i.e. facts and observations) and already know (i.e. models, common sense and knowledge) under certain constraints. In this tutorial, we will (1) describe the motivation of this tutorial and give our definition on machine reasoning; (2) introduce typical machine reasoning frameworks, including symbolic reasoning, probabilistic reasoning, neural-symbolic reasoning and neural-evidence reasoning, and show their successful applications in real-world scenarios; (3) talk about the dilemma between black-box neural networks with state-of-the-art performance and machine reasoning approaches with better interpretability; (4) summarize the content of this tutorial and discuss possible future directions.