Causal inference from observational data (also called real-world data) is relevant in many disciplines, where randomized controlled trials are infeasible, e.g., due to ethical concerns or costs. Examples include medicine, economics, or marketing. However, observational data comes with many inherent challenges for causal inference, which are of both statistical and causal nature. This thesis aims to develop machine learning methods for reliable causal inference from observational data. Examples of planned/completed projects include proposing methods for efficient estimation of (heterogenous) treatment effects in complex inference settings but also developing methods to relax standard assumptions, such as allowing for unobserved confounding. The particular focus is on leveraging and adopting recent advances in deep learning for causal inference, which requires thinking about novel architectures, learning algorithms, and theory. In summary, the work aims at both theoretical and methodological advances, which should empower practitioners from a variety of disciplines to perform causal inference with rigorous guarantees in real-world scenarios.