  Statistical models of real world data typically involve continuous
probability distributions such as normal, Laplace, or exponential
distributions. Such distributions are supported by many probabilistic modelling
formalisms, including probabilistic database systems. Yet, the traditional
theoretical framework of probabilistic databases focusses entirely on finite
probabilistic databases.
  Only recently, we set out to develop the mathematical theory of infinite
probabilistic databases. The present paper is an exposition of two recent
papers which are cornerstones of this theory. In (Grohe, Lindner; ICDT 2020) we
propose a very general framework for probabilistic databases, possibly
involving continuous probability distributions, and show that queries have a
well-defined semantics in this framework. In (Grohe, Kaminski, Katoen, Lindner;
PODS 2020) we extend the declarative probabilistic programming language
Generative Datalog, proposed by (B\'ar\'any et al.~2017) for discrete
probability distributions, to continuous probability distributions and show
that such programs yield generative models of continuous probabilistic
databases.
