In the past decades, machine learning with Empirical Risk Minimization (ERM) has demonstrated great capability in learning and exploiting the statistical patterns from data, or even surpassing humans. Despite the success, ERM avoids the modeling of causality the way of understanding and handling changes, which is fundamental to human intelligence. When deploying models beyond the training environment, distribution shifts are everywhere. For example, an autopilot system often needs to deal with new weather conditions that have not been seen during training, An Al-aided drug discovery system needs to predict the biochemical properties of molecules with respect to new viruses such as COVID-19. It renders the problem of Out-of-Distribution (OOD) generalization challenging to conventional machine learning. In this thesis, we investigate how to incorporate and realize the causality for broader tasks in modern machine learning. In particular, we exploit the invariance implied by the principle of independent causal mechanisms (ICM), that is, the causal mechanisms generating the effects from causes do not inform or influence each other. Therefore, the conditional distribution between the target variable given its causes is invariant under distribution shifts. With the causal invariance principle, we first instantiate it to graphs -- a general data structure ubiquitous in many real-world industry and scientific applications, such as financial networks and molecules. Then, we shall see how learning the causality benefits many of the desirable properties of modern machine learning, in terms of (i) OOD generalization capability; (ii) interpretability; and (iii) robustness to adversarial attacks. Realizing the causality in machine learning, on the other hand, raises a dilemma for optimization in conventional machine learning, as it often contradicts the objective of ERM...