This paper establishes links between determinantal point processes (DPPs) and Monte Carlo techniques (e.g., for application in Bayesian inference), developing new results and insights for DPP-based quadrature methods. The paper is written primarily from a theoretical perspective but also contains numerical experiments. A strength of the paper is that it links various ideas from the relevant literature together in a manner that a NeurIPS audience will appreciate. The reviewers identified some weaknesses in the paper, such as the need to more clearly establish how the results and ideas in the paper are related to prior work. The authors are strongly encouraged to incorporate these suggetsions from the reviewers when revising the paper for the final version.