Causal conclusions are at the center of research, yet notoriously difficult to obtain. Many research studies report correlations only, which, in line with the maxim, do not imply causation. With correlations, one can make predictions. With causation, one can intervene. Paradoxically, causal inference can become harder when more data becomes available. In the by now increasingly common high-dimensional settings which are the focus of this proposal, including all variables is impossible while including too few can severely bias results. Variable selection becomes necessary, yet available methods are in short supply. My aim is to develop Bayesian nonparametric methods and theory for high-dimensional causal inference. Bayesian nonparametrics is eminently suited for variable selection in causal inference, because it excels at both incorporating and describing uncertainty. Recent theoretical advances, in particular in Bernstein-von Mises theory and high-dimensional nonparametric regression, have now finally opened up causal inference to Bayesian nonparametric approaches. I will investigate high-dimensional versions of the two most important causal frameworks, based on unconfoundedness and directed acyclic graphs. I will focus on novel aspects scarcely available in the literature, including uncertainty quantification, a broad range of data types, and nonlinear relationships. My expertise in causal inference, Bayesian nonparametrics, variable selection and survival analysis puts me in a unique position to work on this multifaceted challenge. My dual track in theoretical and applied statistics enables me to identify the problems which have highest priority in practice and are mathematically interesting. The novel methods with solid mathematical statistical foundation resulting from this proposal will tremendously expand the now limited settings in which trustworthy high-dimensional causal inference is possible, with applications in medicine, economics and many other fields.